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Let's derive the equation sin2x + cos2x=1 from the pythagorean formula.   A right triangle with angle x will have a leg that is adjacent to angle x and it will have a leg that is opposite to angle x.  There will also be a hypotenuse.   From trigonometry, a right triangle with a given angle x,  can defined as follows: adjacent/hypotenuse=cosx opposite/hypotenuse=sinx   Following is the pythagorean identity for our right triangle: adjacent2 + opposite2=hypotenuse2   If we divide the above equation by hypotenuse2, we have:   (adjacent2 + opposite2=hypotenuse2)/hypotenuse2 or  adjacent2/hypotenuse2 + opposite2/hypotenuse2=1   Substitute in sinx and cosx into the above equation:   cos2x+sin2x=1   Can you derive the other two Pythagorean trigonometric identities?   cot2x + 1=csc2x tan2x  + 1=sec2x   Hint:... read more

College application essays are one of my favorite assignments to work on with students. They are a chance for me to get to know my students better as we brainstorm topics for their personal essays. I get to hear about childhood memories, unique family traditions, and uncommon hobbies. I love helping students find their voice and tell their unique stories to colleges. My students do not share my enthusiasm for application essays. They feel immense pressure to produce their best pieces of writing to impress colleges. They have also probably heard vague tidbits of advice on how to accomplish this: stand out, don’t be cliché, and be interesting. It’s no wonder that a lot of students have trouble finding a place to start. Here are a few tips to make college application essays less scary: 1. Reading other essays: Read other well-written college application essays. Many colleges release strong application essays from previous years. Reading an array of these essays... read more

A student needed to draw a circle with a 2" diameter, then draw the following angles: 100°, 120º, and 140º. She had her compass but didn't have her protractor.   First she drew the circle, then she drew 2 perpendicular diameters. Since a circle encompasses 360º, each quadrant comprising 90º. We drew the 120º angle first using an entire 90º quadrant plus 1/3 of the adjacent quadrant, erasing the unneeded line, which leaves 60º in that second quadrant.   Then we found the circumference of the circle (C=πD, or 3.14x2"=6.28"). Next we found 1/4 of the circumference (6.28"/4=1.57"). We wanted to be able find the arc length in 10º increments, so we divided the arc of one quadrant by 9 (1.57"/9=0.174"). We converted this into 1/16ths of an inch by multiplying by 16 (0.174"x16=2.79 sixteenths of an inch).   Getting back to our angles, we measured the 100º angle next by taking our remaining 60º and adding 40º of... read more

The journal Science has recently published a meta-analysis of numerous long-term studies examining the correlation between high GRE scores and the quality of work done by graduate students once they are enrolled in doctoral (and in some cases) master degree programs. The researchers--professors of Education at several universities have included there is no evidence that there is a relationship between a high GRE score and "successful" work in grad school; in this case, successful means contributing meaningful, thoughtful, and original work in response to assignments, whether they be short research projects or doctoral dissertations. Another study, in fact, has found a correlation between receiving high scores on the GRE and doing poorly in certain fields of study. This may seem counter-intuitive, but then, so many things are.  I'm not including a link for time limitation reasons, but the study would be easy to track down and read if you insert the appropriate descriptors... read more

If the lesson needs to be cancelled or rescheduled, please inform me through Wyzant messaging atleast 24 hours before the lesson begins. A no-show is a student who is more than 15 minutes late. For no-show students, a cancellation fee equal to the full amount of the lesson will be assessed. If the student is going to be late to the lesson, please feel free to inform me that way I do not consider the student to be a no-show and therefore continue with the cancellation fee. 

Late University of Chicago Professor Emeritus Joseph Williams was arguably one of the best writing instructors of our time.  I met him years ago when he was teaching a judicial writing course at the National Judicial College. The genius of his approach was to improve clarity in legal and business writing, by asking writiers to first sketch a "story" of their work, including the list of "characters" (nouns) and actions (verbs).  By focusing on storytelling, you as a writer are forced to be more concise in explaining information to your reader--in a more active context.  Using the "character-action" approach to writing simplifies your lanaguge, places responsbility cleary for following regulatoins, and reduces your use of the passive voice. Consider these two examples: (Statutory Instrument 1991 No 2680, The Public Works Contracts Regulations 1991, Part 1, 2.4, page 4)   'General saving for old... read more

Tiffany's  Cancellation Fees Listed Below are Cancellation policy and fees for Tiffany G. 1. If you are unable to attend a session that was scheduled, please give written notice through Wyzant 4 hours or more before start time of scheduled lesson. If done so, no charges will be applied to your account. 2. No Show: If you are more than 15 minutes late to an in person session and did not communicate to me why you are late before the session began or during that 15 minutes of tardiness, I will charge the full cost of the session and it is your responsibility to schedule another session and any other session will be charged as per my rate regardless of this missed session. 3. If you are late to any session but it is not considered a no show as per my policy, we can continue the session, you will be charged the full amount, but the time will be deducted from your session (Ie. if the session is for 5PM and you arrive at 5:10PM, the session will still end... read more

Has anyone noticed the profusion (glut) of a questions coming in that are written exclusively in (what I think is) Chinese? (Resources/Answers)   This looks to me like an attack intended to disturb the normal function and use of the WyzAnt site. 

As I have tutored over time via instant messaging, certain problems come up again and again among the students that I have taught English writing to.   As I have corrected student essays over the past few years online, I have developed this set of advice for writers with less experience.  Much of this advice is influenced by Strunk & White's and Payne, so I don't claim much originality here.   General organizational advice for essays: 1. Don’t take the reader’s attention for granted. In the introduction, use attention-getting devices, such as a set of leading questions, interesting statistics, a famous quote from a famous person, a striking assertion or claim, etc. The following sentences in the first paragraph should narrow down the topic to the more specific point made in the thesis. 2. Always put the thesis statement, or main point to be proven or explained, at the end of the first paragraph. Aim to write it as a single sentence, not two... read more

Hi. I'm an English Tutor and I have a question for other English Tutors regarding CBEST essay writing prep.  I was wondering if other English Tutors are challenged by the vast number of EL students trying to pass the essay writing portion of the CBEST.  I would love some suggestions on Grammar helpful for ELL.

As a parent you may be wondering, "How do I find a tutor for my child?" Here are a few questions to ask a tutor: 1. What is your prior experience in ? 2. How will you assess my child's needs? 3. What is your previous experience in education? 4. How will you work in collaboration with my child's teacher? 5. Can you come to my home? Or do I need to come to your location? 6. How flexible are you with your schedule? Is this something you only do part-time, or is this what you do? Here is a list of some questions that a tutor should ask (not in any particular order): 1. What do you think would help your child be more successful? 2. What does the teacher say about how your child is doing up until now in the class? 3. How does your child feel about tutoring? What has he/she been saying about class? 4. How has your child done in previous math courses? When did she/he start struggling? 5. Do you have a copy of the syllabus for the class... read more

How many times have I heard this: "I'm too old to learn Spanish." Or, "Only kids' brains can absorb new languages." While I would like to just say "phooey!" and leave it at that, I've come to see that adults who say such things are in one of two groups: Traumatized Former Language Students, or Victims of Ageism.   There's a problem with language education in America: we don't do it. Why is it that the average person from any African national speaks four or five languages, with no language lab, little money at the local school, and no fancy computer apps? Because the people around them speak multiple languages: It's part of the culture. But also, sadly, it's because of a history of colonialism and the predominance of English in the world. French, Urdu, English, Patois. These folks switch between numerous linguistic codes with utter facility from an early age. It's a natural part of their culture. People in Africa (and Europe) expect multilingualism... read more

  With the wealth of SAT prep materials out there, it can be tough to find the best resources for SAT study. I've been tutoring for the SAT for over a decade, and these are the materials I've found to be the most helpful.     SAT General Study   For all-around SAT preparation, nothing beats The Official SAT Study Guide, published by the College Board. With ten full practice tests, this book contains plenty of study material for all sections of the test. Because the questions are written by the College Board and, in many cases, have appeared on actual administered SATs, they accurately reflect what students will see on test day. (I've never found a test written by a third-party company that comes close to matching actual SAT questions, and I do not recommend third-party practice tests for study.) Working through the questions in this book is the best, most effective way for any student to prepare for the test.   In addition... read more

I am a new tutor so a few days ago when l received a response to one of my first applications, l was very excited. This "student" requested that we talk on phone to finalize the arrangements for date and time.   I told him since l was home on spring break, he could call me on my land line but he wrote back requesting my cell telling him that when l am at home reception is very poor on my cell phone.  He kept insisting on getting my cellphone instead, l was puzzled why.  I never heard back from him.   A day later l got an email from Wyzant that they had determined this not to be a true student inquiry.   I have not figured out yet what this fake student was after.   Can anyone tell me?   Just be aware. Christine M.

Well, okay, it's not incorrect, but it's flawed and by a mathematician's standards: morally wrong.   I'm sure at one point you boringly learned the order of operations. These are the set of rules that tell you whether you should do multiplication before division or addition before subtraction to get the correct answer on your math problem.  1) Parentheses (brackets) 2) Exponents x^x 3) Multiplication 2*2 4) Division 2/2 5) Addition 2+2 6) Subtraction 2-2 7) Get the right answer :)   Except, you don't always get the right answer.   For example: 8-2+1. Is it 5 because 8-3=5? Or is it 7 because 6+1=7?   Is 6/3/3 equal to 2/3 or 6/1?   The issue here is that focusing on the order of operations can lead to ambiguity and obscures the real beauty of mathematics.   A mathematician will tell you that 8-2+1 is actually 8+(-2)+1, which is unambiguously equal to... read more

I am looking forward to visiting Peru again at the end of this month.  This visit will include visits to schools and libraries, including the Biblioteca Nacional, where I hope to see some works housed there, of Inca Garcilaso de la Vega.  Each visit abroad helps me to better understand the language and cultures that I work with in the United States and elsewhere.

This is the story of a certain student who faced a lot of difficulties understanding certain concepts in his class. He/She was at the point of giving up and failing that class when a deep beautiful voice called his/her name out loud, "Student!" He/She didn't understand what was going on. The voice called a second time, "Student, go to the tutoring center!" So the student walked his/her way to the student center and asked for a tutor to help.   The first tutor looked at him/her with an expression of disgust. "How can you not understand this?" the tutor asked. "It is very simple, just do this..." Confused, the student couldn't keep up with the tutor's technique. The tutor seemed to have had a bad beginning of the day and was very impatient. He also got on the top of his nerves, but always seemed to hold back. Scared, the student called onto a second tutor.   The second tutor came with an indifferent expression. He didn't... read more

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