SAT SUBJECT TEST MATH LEVEL 2

PART 2

REVIEW OF MAJOR TOPICS

CHAPTER 1
Functions

 
1.3 Trigonometric Functions and Their Inverses

SPECIAL ANGLES

When you use a calculator to evaluate most trig values, you will get a decimal approximation. You can use your knowledge of the definitions of the trigonometric functions, reference angles, and the ratios of the sides of the 45°-45°-90° triangle and the 30°-60°-90° triangle (“special” triangles) to get exact trig values for “special” angles: multiples of 30°  , 45°  , 60° .

The ratios of the sides of the two special triangles are shown in the figure below.

45° -45° -90° Triangle

30°- 60° -90° Triangle

To illustrate how this can be done, suppose you want to find the trig values of 120°  First sketch the following graph.

The graph shows the angle in standard position, the reference angle 60°, and the (signed) side length ratios for the 30°-60°-90° triangle. You can now use the definitions of the trig functions to find the trig values:

Values can be checked by comparing the decimal approximation the calculator provides for the trig function with the decimal approximation obtained by entering the exact value in a calculator. In this example, sin 120°  0.866 and .

You can also readily obtain trig values of the quadrantal angles—multiples of 90°  . The terminal sides of these angles are the x- and y-axes. In these cases, you don’t have a triangle at all; instead, either or equals 1 or –1, the other coordinate equals zero, and equals 1. To illustrate how to use this method to evaluate the trig values of 270°, first draw the figure below.

The figure indicates = 0 and = –1 (= 1). Therefore,

 which is undefined

 , which is undefined

EXERCISES

1.       The exact value of tan (–60°) is

           (A)  –

           (B)  –1

           (C)  

           (D)  

           (E)  

2.       The exact value of cos 

           (A)  –1

           (B)  

           (C)  

           (D)  

           (E)  0

3.       Csc 540° is

           (A)  0

           (B)  –

           (C)  

           (D)  –1

           (E)  undefined