Chapter 2 Section 4

Chapter 2 Section 4: Values of the Six Trigonometric Functions

Ok guys St. Nick here to bring you the great Six Trig Functions. We already knew 3 of them. Sin ∂=(opp/hyp), Cos ∂=(adj/hyp), Tan ∂=(opp/adj). In this lesson we learn 3 more "Cofunctions" (The "CO" standing for Complementary) These functions are the reciprocal functions of the 3 that we know. The reciprocal to Sine is Cosecant (csc), Cosine is Secant (sec) and Tangent is Cotangent (cot). The equations are: csc ∂=(hyp/opp), sec ∂=(hyp/adj), cot ∂=(adj/opp). As you can see the actual equations are the reciprocals. You can think of it like this: cot ∂ = (1/tan ∂) or cot ∂ =(tan ∂)^-1.
The above equations are in Right Triangle Form. If Coordinate Form is given, it is still relatively easy to find the answers. When solving in Coordinate Form, remember that the Vertical Coordinate is v, the Radius is R, and the Horizontal Coordinate is u. So the sin ∂=(v/r), cos ∂=(u/r), tan ∂=(v/u), csc ∂=(r/v), sec ∂=(r/u), and cot ∂=(u/v).

When asked for exact values you should first find the r, and leave it in radical form, then go about answering the questions.

Above is a chart showing which formula to use in each situation.

Example Problem 1:
Find the exact values of the six trigonometric functions of an angle in standard position whose terminal side contains the given point (8,-5).
First find r. 8²+(-5)²= Square Root (89).
After finding r you can proceed knowing that u=8 and v=-5.

sin ∂=(-5/root(89))

cos ∂=(8/root(89))
tan ∂=(-5/8)
csc ∂=(root(89)/-5)
sec ∂=(root(89)/8)
cot ∂=(8/-5)

It may help if you visually if you graph this.

Sample Problem 2:
Find the value for the given trigonometric function (on your calculator).
cot 126˚. To find this you would have to find tan 126˚. Then either find the inverse (x^-1) or do 1/(tan 126˚). The answer would be -.7265

Here is a website with some additional resources.

http://people.hofstra.edu/faculty/Stefan_Waner/trig/trig2.html


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