Isaak is approved to conduct lessons through Wyzant Online. Wyzant Online allows students and tutors to work remotely via video, audio, and collaborative whiteboard tools. For more information about how online tutoring works, check out Wyzant Online.
If you’re interested in online lessons, message Isaak to get started.
University of Alberta (Engineering Physics)
I hold a Bachelor's degree in Engineering Physics from the University of Alberta. The U of A is one of Canada's largest universities and a top engineering school. I developed skills in math, physics, programming and controls theory there.
I also learned a lot about engineering through participation in student engineering competitions. I joined teams that engineered, promoted and tested conversions of a Ford Taurus and a Dodge Caravan. The Taurus became a hybrid electric vehicle. The Caravan ended up a liquefied propane vehicle. At that time these technologies were future targets of big automakers not yet in production. Driving non-stop through Montana, Wyoming and Colorado was another memorable experience. The dual-wheeled pick-up truck pulled our LPGV van in a mysterious looking trailer. Far some reason, we ended up first on the schedule for pre-competition testing in San Antonio. The appointment seemed far too soon after our last final exam. There were some interesting mishaps along that trip. We had to make some unexpected last-minute adjustments on our vehicle. I had bought some standard components along our trip. I had no choice but to pull an all-nighter in the hotel in San Antonio. We needed to construct and install a fuel-pump timer-controlled circuit designed to help us pass the hot-start test. With my teammates we were able to find a spare fuel pump and some switches suitable for a test-bed. I was able to develop a robust functional circuit by morning. This required a combination of math, physics, electronics, testing, and trouble-shooting. With careful teamwork, we got the circuit installed in the actual vehicle on time. We tested the installation with baited breath. It worked! The competition made stops at College Station, the Texas World Speedway, and Austin and was a great success. After all that stress and a fun, but jam-packed schedule, our tired team headed home. We took the long way back to Edmonton to accept promotional invitations in Oklahoma and Minnesota. What an experience!
My tutoring experience includes five years of tutoring through Wyzant. You can understand from my background why I prefer to tutor math or physics courses. I am well qualified to tutor from high school through at least the first/second-year college-level. On occasion, I also tutor other courses or subjects. Some examples are electrical engineering courses, chemistry, statistics, programming, even ESL. I provide tutoring with a patient, courteous and professional demeanor. I strive to help students develop their knowledge. I myself am an inquisitive, creative person and a lifelong learner. I still take courses online and I frequently consider earning an advanced degree to be able to teach in college. I would probably be a high-school teacher now but for citizenship requirements. I have no desire to give up Canadian citizenship and I feel like I still owe it to Canada not to. Too bad the U.S. does not recognize dual citizenship!
When students meet or exceed their goals, I am glad. It is important that everyone give their best effort throughout life, and school is a great place to start. Without broad and successful education of each generation, how long can we even expect to live in a viable world? How important is education in the interest of fairness, justice, beauty and peace?
A typical tutoring session naturally cycles through question, explanation, demonstration, and application stages. Ideally, a student should use a tutor to augment rather than replace their study efforts. Students who rely on help from a tutor for every problem short-circuit their own success. While I sometimes work through a problem with a student, I avoid providing answers to problems. My goal is to work with the student to ensure they understand the raw concepts, and learn to apply the concept. I am also willing to work with students who understand the concepts but want to strive for better marks. These students sometimes have questions that reach beyond the core material.
I am flexible to work with the student and adapt the session to the student's needs.
A student should maintain the momentum reached during the session by practicing on their own. I would recommend studying a problem until the entirety of the correct solution makes sense. You can assert that the solution makes enough sense to you once you are able to explain the solution to someone else. You should be able to answer frequently asked questions about the problem without your text or notes. You are welcome to send me a text, email or phone call about a problem when a question comes up; I will be glad to help.
The ideal tutoring environment differs from student-to-student. If the noise-level in a coffee shop or cafeteria does not bother the student, a coffee shop could be ideal for that student. White crowd noise can sometimes be comforting, familiar, and invigorating. If the student prefers a quiet environment, meeting online might be ideal. Noise-canceling headphones can make online meeting rather conducive for concentration. A library's tutoring room might be ideal for sensitive students. A student's home is where some students work best.
I am also willing to help athletes explore or train for sports such as volleyball, basketball, badminton or the mile. I helped represent my high-school competitively in each of these sports and School-reach. Our teams received state-level medals in School-reach and in our division of volleyball. In high school, I was a middle hitter/blocker and considered the best passer by the coach. I was also a player/coach in a recreational league, sometimes playing setter, and played a lot of beach volleyball. Ice hockey, soccer and ultimate are also among my favorites. My services might be ideal for the athlete or small group of athletes that are exploring a new sport. I could also help a team who needs a replacement or substitute coach at short notice. I hold a Bachelor's degree in Engineering Physics from the University of Alberta. The U of A is one of Canada's largest universities and a top engineering school. I developed skills in math, physics, programming and controls theory there.
I also learned a lot about engineering through participation in student engineering competitions. I
Isaak is approved to conduct lessons through Wyzant Online. Wyzant Online allows students and tutors to work remotely via video, audio, and collaborative whiteboard tools. For more information about how online tutoring works, check out Wyzant Online.
If you’re interested in online lessons, message Isaak to get started.
Awesome tutor. Isaak doesn't get frustrated at all. He works hard until you get it and the work is done. Thank you Isaak.
Isaak was very helpful in preparing me for my midterm physics exam. I appreciate his patience and ability to help me through physics problems. He helped me become more confident in test taking.
It was my son's first tutoring session with Isaak. He found his time with Isaak very beneficial and is looking forward to his next session with him.
With a big test on Monday and a lot of unanswered questions, Isaak came through big time with a tutoring lesson on the Saturday right before, to help clear things up for our daughter. While many students evidently failed the test, our daughter was one of the few able to notch a "B" on a very complicated exam. Thank You Isaak for fitting her into your schedule and meeting us on Saturday! It made all of the difference. We would definitely call you again!
Helped me prepare for an exam that i thought i was going to fail. In electrical engineering but i came out with a 75!! he was patient and taught me the core basic of each problem
In the last 2+ hour session I was impressed by the range of control systems covered and the ease in which Isaak was able to handle them. He had helpful explanations from trigonometry all the way to tricks for eliminating error in higher order systems. These sessions have been as helpful as my three hour a week lectures at my University. In addition, my increasingly strong knowledge in control systems has already gotten me job prospects. I can't say enough about Isaak's tutoring. One final note, I have noticed that he prepares before we meet so that he is familiar with the topic and can guide me through the trickier portions of the problems. This is priceless because it allows me to create a mental structure on how to solve certain types of problems that is clear and concise and on which I can call on when tackling future problems. Thank you Isaak!
He went very much into detail and obviously knew the material on force vectors! I would love to recommend him to anyone interested!
Very excellent teacher, patient with you, shows you in away that is easy to understand, and will not move on unless you fully understand the problem at hand.
Worked with Isaak virtually. Although we had connectivity issues (likely due to me), he hung-in there with me and we finally got connected. Very helpful. We will likely use him again to help my daughter with Physics.
I appreciate your positive feedback. We did use up an hour of your time and my time (which I refused payment for), but at least it worked in the end, your daughter was using the time for other homework, and we were able to get a short physics session in.
I wrote a blog about tips for newcomers to online tutoring in the hope it will help others first collaboration with a new online tutor experience go more smoothly.
He showed me my weakness. Thank you although I still have some problem or more problem especially about mathematics. I am thankful to have him help me with my homework.
It's difficult to find a tutor who is as patient and thorough as Isaak. In only a day, Isaak helped me cover convolution, fourier series and transforms, and the basic concepts that that revolve around these concepts. He was flexible with scheduling and material; he even tutored me at 6am to help me review before the test! You definitely want Isaak on your team if you're struggling with complex math problems and concepts.
Isaak came over last night on last minute call. He worked with our son for a test today. He was very nice attending our needs for last minute call.
Very knowledgeable of the content.
Isaak has been tutoring me in Citcuit Theory and Design. He is an incredible tutor. He is patient, helpful, and seriously knows all his stuff. He flows through the material perfectly. He has helped me go from being totally lost to actually knowing which steps to take next in a matter of weeks. I highly recommend Isaak to anyone and everyone!
Isaak was great- made time for me at the last minute, and was patient with my repetitive questions. He is an excellent tutor!
Isaak helped my 10th grade child to get ready for his up coming test at his Physic college course. They studied the physics principles behind buoyancy (Archimedes principle: the buoyant force is equal to the weight of the displaced fluid), pressure (force/area), and applications to buoyant forces on objects in gases as well as the traditional underwater buoyant forces. etc. Isaak was very professional, patient and knowledgeable about the material. I am certain that I will look into hiring his service again. Such a great turtor!!. THANK YOU SO MUCH ISAAK.
Thank you for being available in such short notice. Your assistance helped me think through the problems we went over and my remaining problems.
Very flexible and patient. Not only knowledgeable, but able to pass that on and make something complex seem simple. I had concerns about getting and using a tutor, especially as an older student, he proved them unfounded. Concepts I had struggled with for days were cleared up in minutes. If you are considering a tutor, you will not regret working with Isaak.
Isaak was able to provide tutoring in physics to my daughter and he was able to work through constant acceleration such that she was able to capture the concept. We are looking forward to utilizing his help in the future.
Isaak is an amazing tutor who is able to translate his physics knowledge into an Aerodynamics lesson (though, never taking the course himself) almost overnight. Most impressively, Isaak accepted and excelled in this role as a tutor for a college level, eight week accelerated term student during the seventh week for a course at Florida Institute of Technology. I am absolutely astounded with the results of our session and the follow-up! I would recommend Isaak to anyone taking Physics or Aerodynamics!
Every word in Isaak's profile is true - he knows his math. I came to him with a difficult AP statistics problem and his reply made sense to me. Finally, I have someone I can work with if I need advanced help. I am recommending him to others for sure!
Isaak helped me in honors geometry. We worked on the study guide for an upcoming unit exam. He was very patient. Not only did help me master the material, he also showed me some tricks to increase my speed. We are very happy with WyzAnt and with Isaak.
Thank you Isaak for the great session this morning! You provided patient support and made things much easier to understand. We have an increased level of confidence for the upcoming test and will definitely be scheduling future sessions. We highly recommend you!
Isaak, your help has been an instrumental part of my learning this semester and I appreciate all the effort and time spent.
I contacted Isaak to help me with understanding a paper on error-correcting codes, and he did a great job walking me through the more difficult-to-understand sections of it within the hour. The example encoding and decoding that we worked through, worked especially well for helping me see what was going on.
Jake felt you were excellent which is the best result for us. Thanks, Isaak, we look forward to working with you over the next 18 months.
Isaak was very thorough and taught me the quickest way to solve problems in Math. He worked with me on many different topics and reviewed techniques. He pointed mistakes quickly and taught me the correct way to solve. He is a great tutor!
We went over Laplace Transforms and convolution. He helps me understand material at a deeper level, starting from its roots.
He explained things to me so that I understood them. I finally learned something I have been trying for a long time.
Thanks to Isaak's tutoring, my daughter scored the highest on her final exam than she scored on anything else all year. She said she will definitely call him in the future when she needs help.
Isaak put my son at ease. Showed him a different way to look at the Trig formulas and how they related to each other. Post session write up was invaluable. Let us know where he thought the gaps in understanding were and gave us additional practice resources to use between tutoring sessions.
Isaak has been very helpful. He's patient and has the ability to break down concepts that are not so straightforward. He's been great working with my son!!!
My son enjoyed working with Isaak B. for his physics course at the University of Pittsburgh. My son's physics teacher was very hard to understand. Isaak was able to simplify this difficult course and my son received an excellent grade. I recommend Isaak as a physics tutor. Isaak is a reputable and reliable tutor.
Isaak tutored me for the quantitative portion of the GRE via Skype. We worked together for about a month for a total of about 14 hours. My score skyrocketed. Isaak is very patient and knowledgeable about a breadth of subjects. I highly recommend him.
Isaak has been working with my son for the past two weeks with his AP calculus. He goes above and beyond what I expected from him as a tutor. He gives very detailed reviews of each lesson they have together. He is very patient and understanding. I would highly recommend him if you need any help.
Isaac is very easy to reach by text or phone. He is aware of my son's needs in terms of atmosphere and has made suggestions to maximize my son's tutoring experience.
Isaak B. is an incredibly qualified, willing, and patient tutor. Additionally, he tries his hardest to be as accommodating and as accessible as possible.
I needed his help in a pinch online for precal. He was very helpful and helped me do well on my test review.
Isaak is very knowledgeable. My daughter seemed to see Physics in a whole new light after spending time with him. I would not hesitate to recommend him.
Isaak and my daughter seemed to be talking the same language (math) in an insightful and enthusiastic way. Certainly, the 2 hour lesson was very helpful. My daughter will continue taking lessons with Isaak to review different materials to start preparing for the final exam, as well as current material that she needs to master. She enjoyed very much the lesson and is looking forward to the next one.
Isaak helped my daughter a lot with her Physics during their first session. Very knowledgeable and patient. I'd highly recommend him.
Our son was "down" because he was struggling with his homework and the concepts taught in his class. After 90 minutes with Isaak, our son was excited about now understanding and how Isaak helped him. Isaak coached him instead of giving him the solutions. Our son's whole demeanor changed after this session. Great job Isaak!
Isaak is very patient and insightful with our son. Our son loves him and has really improved under his tutelage.
Isaak is incredibly smart and can help you see problems in a different way. He has been a great help for preparing both for the SAT subject tests and the ACT. We will also reach out to him if we need help in Calculus this year.
Isaak has been a wonderful tutor for our daughter. She is a bright student but really hit a wall with Algebra 2. He is able to evaluate the trouble spots and give her confidence to the new skills needed. He is very strength based and also able to target learning areas.
Thank you, Issak, for helping our daughter with Earth Science. She feels much more comfortable with the material and has a better understanding of the lesson taught by her teacher.
Isaak has been a great tutor for my son. He was failing trig, in the beginning of 11th grade, now half way thru the school year with help from Isaak, he has come up to a high "C". He probably could get a "A", if he did his homework. lol. But at least he is understanding it now, thanks to Isaak. Isaak is very patient and kind tutor. He is always on time and if you ever need to get a hold of him, he is very easy to contact, thru his cell phone. He also is very accommodating to your schedule. There has been a couple times, that my son has forgotten his book or homework papers at school, and Isaak, was creative enough to still have a good learning lesson for him. He also is really comfortable with Isaak. He is very well mannered and just a nice young man, I would recommend him to any of my friends for tutoring their child. I feel lucky that we found him. Plus, a tutor that comes to your house and one on one with your child is an added plus!
Isaak is not only a great content-tutor, he also possesses a professional demeanor that helps instill our sense of confidence in him. I think he's a good influence on our son's scholarship, study methods.
In most cases, tutors gain approval in a subject by passing a proficiency exam. For some subject areas, like music and art, tutors submit written requests to demonstrate their proficiency to potential students. If a tutor is interested but not yet approved in a subject, the subject will appear in non-bold font. Tutors need to be approved in a subject prior to beginning lessons.
The ACT math test can be challenging exam to prepare for, especially for students who completed the relevant high school math courses significantly earlier than their test date. It tends to have broader expectations on the depth of math knowledge, especially geometry, than does the SAT, which could catch unprepared students by surprise. I have recently worked through the math and geometry review section of an ACT math prep review book with students who needed a crash course. I have not yet encountered ACT math questions I could not answer, and I would be glad to help anyone who could benefit from additional help.
I am able to help students who, for whatever reason, fall behind their expectations in algebra I. The polynomial and rational functions, exponents and logarithms, radical expressions, factoring, polynomial division, and equation-solving skills and principles studied in Algebra I are foundational skills for investigators in science, managers optimizing business decisions, engineers improving a design, or software developers cracking open new concepts.
As an engineer, I routinely use the skills and principles taught in Algebra 2! Exponents, logarithms and roots come up all the time because many relationships between important factors in a design or description of a natural principle can only be treated as if they were linear, or that is, adequately described using straight lines, to the roughest of approximations. Not having these mathematical tools would make engineering work rather crude. Imagine how the drawings of a Corvette would look if the artist were restricted to use only straight lines!
Similarly, complex numbers are very useful for describing periodic waveforms, predicting natural resonances in systems, designing control systems and many other things.
I enjoy helping students understand and master the challenge of solving equations involving one or more of these non-linear equations, systems of linear equations.
Calculus includes a wide range of powerful mathematical applications based on the idea that many types of analyses work better and reveal more interesting and useful truths (in many cases, surprisingly simple but non-obvious ones) when we exploit the ability to divide regions of interest into an unlimited number of small parts. Many of the most famous results students have learned in other parts of math and science, such as the volume of a sphere, for instance, were discovered using simple calculus techniques. Students expecting to earn credit for calculus in college should anticipate that topics of study to follow in latter courses will use calculus. Also certain kinds of homework problems one is expected to solve in upper-level college courses will use basic calculus skills.
I tutor calculus at the level typically taken by high-school students, college freshmen and college sophomores. This includes high school calculus, AP calculus AB/BC, business calculus, calculus of sequences and series, multi-variable calculus and ordinary differential equations.
I also took partial differential equations and complex-variable calculus courses (but do not feel comfortable tutoring those).
I earned top marks in high school chemistry and completed the two college inorganic chemistry courses standard to most engineering programs with above average grades. I also took several related courses over the course of earning my engineering physics bachelor's degree, including classical thermodynamics, engineering thermodynamics, and statistical thermodynamics (acing the final!). Recently, I also completed a Stanford MOOC on photovoltaics and battery chemistry, which improved my understanding of the topic immensely.
Chemistry education has certainly improved significantly with the advent of the information age, and I have enjoyed tutoring chemistry. I generally prefer to limit my chemistry tutoring to those students who also occasionally need math, physics, or test prep help.
I am qualified to teach statics and dynamics , calculus, physics, circuits, and can often help students who have questions in linear algebra, or inorganic chemistry.
These first-year engineering courses common to all branches of engineering are all courses that I passed with good grades in the course of earning my engineering physics degree. I also did well in my strength of materials course and my mechanics of rigid bodies course (2nd year courses in common with most engineering disciplines).
Differential equations, and their digital counterpart, difference equations, are hugely important to the study of many fields.
I can help any calculus student learn to solve separable ordinary differential equations, non-separable first order linear equations, second-order linear ordinary differential homogeneous equations with constant coefficients. Students often struggle with the methods of underdetermined coefficients, variation of parameters, and transform techniques such as Fourier transforms, and Laplace transforms. I can help because my degree included all of this material, much of which was applied later in several engineering courses.
Some of the fruits of electrical engineering are ubiquitous throughout modern society, while other aspects of it play behind-the-scenes. Electrical/electronic engineering includes the analysis of circuits, motors, transmission lines, semiconductor devices, digital circuits, analog circuits, control systems, power conversion, micro-processing, control theory (classical, modern, and digital), electrostatics, electrodynamics and others.
Each of these topics is deep enough to make up one or more courses all by itself. I am well-qualified to teach introductory circuit analysis of AC/DC circuits; it is the basic glue that every electrical engineering -related degree-holder knows like the back of their hand. I have helped students struggling with digital circuit theory and boolean algebra, MOSFET logic circuits, amplifier design, control theory, etc.
Geometry is a fundamental tool with which it is important for every student to be familiar. I help students who have difficulties constructing geometrical figures using a straight-edge and a compass. I understand geometrical theorems and can demonstrate constructing geometrical proofs that require the conjunction of several of them.
I can inspire students to consider the material relevant by recounting some of the roles geometrical arguments play in practical applications in engineering, science, business, medicine, and sports.
I have worked with a small number of other undergraduates or bachelor's degree holders preparing to take the GRE. Perhaps math has never been your strong suit or perhaps you did ok or even excelled in math at one time, but didn't use much math in your program or maybe only in freshman year. It happens to many GRE applicants! I have the patience and the time to help anyone recover (or if necessary, develop) mathematical skills necessary to excel on the quantitative portion of the GRE. My first GRE student left me what I consider a very positive review. I tutor a lot of math which is more demanding and a wide variety of math courses. This is probably partly why I am able to tutor GRE quantitative section effectively despite never having taken the GRE myself.
Linear algebra is the study of systems of equations described using matrix and vector notation.
It can seem like a chore before you realize the practical applications of it, but it is a chore worth doing well, as it has myriad applications throughout engineering theory.
The knowledge of linear algebra simplify the task of solving simultaneous equations. This is ginormous! Why? Because simultaneous equations arise that need to be solved to do structural design in civil engineering, circuit design in electrical, lens design in optics, control systems design. Aspects of it are used in physics to solve quantum mechanical equations, in mechanics to find torque vectors or moments, .... etc.
In short, there are untellable numbers of applications, but you'll run into applications of linear algebra time and time again, so learn it thoroughly the first time!
I have a degree in engineering physics. This is an engineering degree that is similar to electrical engineering. I am qualified to tutor mechanical engineers in any of the first year courses (since these courses are common to all branches of engineering) such as calculus, linear algebra, statics, dynamics, physics for engineers, electric circuits, possible vehicle dynamics and control, etc. In some circumstances I may be able provide some assistance with understanding higher level mech e topics in heat transfer, thermodynamics or fluid dynamics.
I have worked extensively with several versions of Excel (although not with the latest). In conjunction with my background as a software developer, I can readily handle comprehending and exploiting some of the most obscure features of the package, including the use of plug-ins, VBA, writing macros and setting up spreadsheets with custom formatting. I have set up numerous Excel spreadsheets over the years. I use it to help me do my taxes every year, to explore and compare various alternatives when making decisions at home and on the job, and to analyze data (even in three dimensions) including curve-fitting and statistics.
Powerpoint is a Windows application designed to help you produce effective, readable, and attractive slide presentations. It can also help you apply an overall theme to your entire presentation, so that you can experiment with and customize the color scheme and choose from a variety of styles and animations to help jazz up your presentation. Video and music can easily be incorporated and accompanying handouts can be customized in myriad ways (although not always appropriate depending on the purpose, audience, and circumstances). I am qualified to tutor someone in Powerpoint because my most recent Powerpoint presentation drew specific praise for being a very effective use of the tool. If I recall correctly, I believe it was about a physics experiment on blackbody radiation. My background as a software developer often gives me special insights into the inner workings of such packages to allow me to notice, understand and explain behaviors and functionality that sometimes seem nonsensical to the average user.
I developed strong problem-solving skills while earning my bachelor's degree in engineering physics at the University of Alberta. My degree's requirements included some physics courses taught by the Physics department.
Precalculus is an important and interesting part of every student's life if they are considering taking calculus, arguably the most useful mathematical tool ever invented (and by reputation, perhaps the most intimidating).
Building a solid foundation in the trigonometric relations, the relations between the manipulations of an equation and its graph, inverse functions, composite functions, domains, ranges, roots of polynomials, and the like ensures that the study of calculus will not become far more difficult and intimidating than it needs to be. Focus on doing well in precalculus so that you can get through calculus without a headache!
The SAT Math test is typical of many standardized math tests in that often as not, two or more of the typically four offered answers can be eliminated if one knows some of the most important math shortcuts -- simple facts and observations that can save time or improve accuracy.
In most cases, I coach students to put their calculators away. Most SAT questions can be answered correctly without pressing a single key. Only after all questions have been attempted would I normally consider checking work with a calculator.
To improve SAT math scores, I work with a student to make sure their understanding of the subject is strong, and help work the kinks out of any identified weaknesses in the tested skills. Solid understanding is a prerequisitie of sane confidence, a prerequisite to keeping exam stress within healthy and helpful bounds.
Even though I have never myself encountered a need to take a course purely dedicated to statistics, I have successfully tutored students struggling with concepts in statistics. Perhaps this is because I am very good at math, and tutor a lot of it, and therefore easily understand all of the math involved. It is partly because I have in the past signed out and studied statistics textbooks from the library in order to make sure I was prepared enough to help the stats students who had nowhere else to turn. Finally, part of earning my bachelor's degree in engineering physics required passing a course called "Statistical Thermodynamics" in which I learned about how the statistics of the motions of atoms in a gas, or atoms in a magnet, or molecules in a rubber band, for instance, can be used to help us study various aspects of our world and predict certain properties of it. I earned a perfect score on the final exam in that course. I also encountered aspects of statistics in other courses such as quantum physics, laser electronics, control system theory, and certain physics laboratory experiments.
Trigonometry is useful for making measurements of existing things, planning future things, and implementing the planned things. Navigation is a good example of a task involving all three and is an essential part of many kinds of work, with or without college degrees. One must establish locations, plan routes and follow headings even when sufficiently accurate, quick, reliable and affordable technological aids are not available. In any case, sophisticated technologies like GPS and other measurement systems intend to augment rather than replace one's understanding of angles and directions. The skill-set offered by trigonometry directly benefits everyone who must move or manipulate within our three-dimensional world.
The relationships between the sides and angles of a triangle are also crucial for students to learn for more abstract reasons. These relationships provide a basis for understanding and describing other shapes. Trigonometry helps describe familiar two-dimensional shapes such as lines, circles, ellipses, and hyperbolas as well as familiar three-dimensional shapes like spheres, prisms, pyramids, and cylinders. Trigonometric skills are necessary to work with fancier two-dimensional shapes such as cardioids, limacons, roses, cissoids, foliums, cycloids, and conchoids. These skills also simplify the description of complex three-dimensional shapes such as spheroids, hyperboloids, and spirals. Most generally of all, a powerful technique published by Joseph Fourier in the early nineteenth century breaks arbitrarily complex waveforms into combinations of the trigonometric functions. This technique, called Fourier analysis, is fundamental to several engineering, scientific and mathematical applications. The knowledge of the properties of triangles and familiarity with each of the trigonometric functions helps future college graduates, tradesmen, and artists alike.
Although business calculus courses typically omit the use of trigonometric functions, students pursuing degrees in engineering or science must take a full-fledged version of calculus. They are expected to know and understand trigonometric functions and identities before they begin.
Understanding triangles can help students planning to work in various trades. Advanced electric work (as a journeyman or master electrician, or with electronics) involves trigonometry because the math needed for understanding the measurement of alternating-current electricity requires it. Other construction jobs, such as welding, machining, carpentry, stonework, landscaping, earthwork, and plumbing, use trigonometry for making measurements, estimating costs, and constructing precise angles.
Trigonometry has pragmatic value to artists such as sculptors, animators, painters, and photographers. Artists exploiting their knowledge of triangles and more advanced shapes produce more beautiful sculptures, paintings, animations and photos than their competition.
While a full-time university student, I player-coached a men's volleyball team that started with some rank beginners and level 15 (= last) of a bubble-up/down-type weekly city-wide recreational volleyball league up to around level 10 in only one year.
I made use of my high school experience, in which I was voted athlete of the year largely on the strength of being a key player of a two-time provincial bronze medal-winning team, including an undefeated regular season my senior year, as well as training obtained from the coaches and players of the collegiate teams of the University of Calgary Dinos, and the internationally-ranked University of Alberta Golden Bears, including "Most Improved Player" from renowned U of A coach, Terry D. as a member of an adult summer volleyball camp. While I cannot exactly claim to have developed the skill set of an indoor-game setter, I also accumulated several games worth of two-on-two sand court experience, in which setting skills are particularly important, and I often serve as the setter in typical pickup games.
I am nevertheless undoubtedly skilled enough to help many players improve their float serve, jump-serve, hitting, passing, court vision, blocking, and team play.