Image 78k

GeoGebra sketch for http://www.wyzant.com/resources/answers/27895/sin_x_6_cos_3x_4

Image 78k

GeoGebra sketch for http://www.wyzant.com/resources/answers/27895/sin_x_6_cos_3x_4

Image 65k

Sketch for http://www.wyzant.com/resources/answers/27349/solve_for_x_sin_inverse_x_sin_inverse_2x_pi_3

I am happy to announce that all my students have passed the NY State Regents examinations, except one student. The subjects varied from Algebra 1, Algebra 11/Trigonometry, English, US and Global History and Living Environment. I am so proud of them. Most of these students are students who struggled quite a bit. It was a long journey but one I would do again. I... read more

Here are some of my favorite Math resources. Check back again soon, this list is always growing! I also recommend school textbooks, your local library, and used bookstores. As a note, college-level math textbooks are often helpful for high school math students. Why is that? Isn't that a little counter-intuitive? Yes, it would appear that way! However, many college-level math textbooks... read more

http://www.wyzant.com/resources/lessons/math/trigonometry/polar-and-rectangular-coordinates I am not done with it yet. I still need to show how simple it is to do the "same" calculations in the second, third, and fourth quadrants.

Hi All! In the spirit of giving, starting on 11/29/2013, I will be offering a few brainteasers/ trivia questions where the first 3 people to email me the correct answer will receive a free, one hour, tutoring session in any subject that I offer tutoring for (via the online platform)! That's right free! Get your thinking hats on everyone! Merry Christmas... read more

I was working with a student today, and as we worked through the section in his book dealing with Trigonometric Identities and Pythagorean Identities, we stumbled across a problem that gave us a bit of trouble. The solution is not so complicated, but it sure had us stumped earlier. The problem was presented as such: Factor and simplify the following... read more

Buckle up readers, it's Trig time! Trigonometry can be scary to many students, and in my opinion, a lot of that is because one of the most confusing concepts in trigonometry occurs right at the very beginning, in the form of the Unit Circle and Radians. Let's start at the beginning. Give yourself a circle with a radius of 1. Now center that circle on the origin... read more

Trigonometric Exponential Functions Written by tutor Danielle R. Exponential functions are typically used to model natural phenomena that increase or decrease at an exponential rate. For instance bacteria and many other populations can grow at an exponential rate. The amount of radioactive substances will normally decrease at an exponential rate. The way we calculate interest is an exponential... read more

Reciprocal Identities Written by tutor Jeffery D. A brief summary The reciprocal of a term a/b is defined as b/a. If we let a = sin(x) and b = 1, and then take the reciprocal we obtain 1/sin(x). Similarly, if we let a = cos(x) and b = 1, and then take the reciprocal we obtain 1/cos(x). Recall that tan(x) is defined as sin(x)/cos(x). Taking the reciprocal we obtain cos(x)/sin(x)... read more

Pythagorean Identity: a non-technical explanation Written by tutor Jeffery D. Before you learn about trig identities, there are few things you need to know. No, really. As you have probably experienced when studying other maths, you know that math builds on itself. So, please take a moment to review these few concepts to be sure that you understand what they mean. Trust me on this, otherwise... read more

Converting Between Polar and Rectangular Coordinates Written by tutor Barbara W. What are rectangular and polar coordinates? They may both refer to the same locations (or points) on a chart or graph. I liken rectangular coordinates, sometimes called Cartesian coordinates, to city walking directions and polar coordinates to airplane flying directions (“as the crow flies”)... How... read more

Logarithmic Functions Written by tutor Kira L. A logarithmic function has three main components. The first component is the base, b; the second component is the fixed value, y, which is what you input into the function; and the third component is the output of the logarithm function, x. The output of the logarithm function is the answer to the following question: to what exponent must I... read more

Law of Sines Written by tutor Carol B. The law of sines is a proportion used to solve for unknown sides and/or angles of any triangle. In any triangle, the ratio of a side length to the sine of its opposite angle is the same for all three sides. Law of sines formula: a/sin A = b/sin B = c/sin C Use the law of sines if (1) one side length and its opposite angle measurement... read more

Inverse Trigonometric Functions Written by tutor Lauren B. What is an Inverse Trigonometric Function? An inverse trigonometric function is a function in which you can input a number and get/output an angle (usually in radians). It is the inverse function of the basic trigonometric functions. Notation: The inverse function of sine is sin-1(x)=arcsin(x), read as “the arcsine of x.”... read more

Trigonometric Double-Angle and Half-Angle Formulas Written by tutor Michael B. Objective In this section, you will learn formulas that establish a relationship between the basic trigonometric values (sin, cos, tan) for a particular angle and the trigonometric values for an angle that is either double- or half- of the first angle. These relationships can be very useful in proofs and also... read more

Converting Radians to Degrees Written by tutor Yvonne H. If you are wondering how to convert from radians to degrees, then you probably have some experience converting from one unit to another. For example, you probably know how to measure the length of your bedroom in feet and convert those feet into inches, i.e. 18 feet = 18 X 12 = 216 inches long. The same concept, unit conversion, applies... read more

Complex Numbers Written by tutor Colin D. How to Envision Complex Numbers Graphically: The Complex Plane The complex number x + yi corresponds to the point with coordinates (x, y) The x-axis is the real axis The y-axis is the imaginary axis Real numbers are associated with points on the x-axis For example:... read more

Acute angles, right triangles, and trigonometry Written by tutor Jessica G. An acute angle is one whose measure is less than 90 degrees. An acute triangle, therefore, is a triangle whose three angles each measure less than 90 degrees. An equilateral triangle is a specific type of acute triangle where the three angles have an equal measure of 180°/3 = 60°. A right angle, formed by... read more

Trigonometry Do you like studying angles and triangles? Then you'll love learning trigonometry! Trigonometry is a branch of math that looks at the relationships between side lengths of triangles and their corresponding angles. You'll be able to use your knowledge of geometry and algebra to derive and employ the trigonometric identities. Trigonometry is essential to the understanding... read more