## Trigonometry Math Tutoring

There are common questions that students have in algebra. We answer here a couple here on the following topics:

Definition of Sine and Cosine Functions

Definition of Other Trigonometric Functions

We are willing to answer other questions for you. Click on the "Contact Us" tab above and we will post an answer.

**DEFINITION OF SINE AND COSINE FUNCTIONS**

Kendra asks, "I get so confused with the definitions of the trigonometric functions. How are the trigonometry sine and cosine functions defined?"

Kendra, to answer the question, let us together do the following:

- First make a coordinate plane by drawing a horizontal x-axis and then a vertical y-axis. Let us name the origin point O (0,0)
- Locate, that is plot, a point P (x,y) any place on the coordinate plane. That can be in any quadrant.
- Name the x-intercept point Q (x, 0). That is, the point on the x-axis directly above or below point P (x,y) is Q (x, 0).
- Now you have formed a right triangle OPQ with a right angle at point P.
- Calculate the distance between point O and point P either by using the distance formula for the distance between point O and point P or using the Pythagorean Theorem. Name that distance r where r is .
- For angle POQ, name the side PQ the opposite side, side OQ the adjacent side, and side OP the hypotenuse of the right triangle.

Then we define the following:

**sin POQ** **=**** y**** ****/ r = length of the opposite side / hypotenuse.**

**cos POQ** **= x / r = length of the adjacent side / hypotenuse.**

**DEFINITION OF THE OTHER TRIGONOMETRIC EQUATIONS**

Matt wants to know, "Is there an easy way to remember the definitions of the tangent, cotangent, secant and cosecants?"

My experience is first to learn the definitions of sine and cosine that I have above. Then use the following definitions:

**tan POQ = sin POQ / cos POQ** **=**** y**** ****/x = length of the opposite side / length of the adjacent side**

**cot POQ = cos POQ / sin POQ** ** = x**** ****/y = length of the adjacent side / length of the opposite side**

**sec POQ = 1 / cos POQ** ** = r**** ****/x = hypotenuse / length of the adjacent side**

**csc POQ = 1 / sin POQ** ** = r**** ****/y = hypotenuse / length of the opposite side**

Cody asks, "Are there good algebra review and pre calculus videos?"

Cody, there are great precalculus and trigonometry videos at Khan Academy. Click on http://www.khanacademy.org/. Then scroll down the page to the following topics:

Precalculus: Videos of the more common precalculus topics students want help with.

Algebra I Worked Examples: Sample problems worked from Algebra I.

Trigonometry: Includes videos of some basic trigonometric topics in your precalculus.

Linear Algebra: Includes great videos on matrices and vectors.

ck12.org Algebra I Examples: Great review videos to make sure you understand Algebra I topics.

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