SPECIAL ANGLES

SAT SUBJECT TEST MATH LEVEL 2

PART 2 REVIEW OF MAJOR TOPICS

CHAPTER 1
Functions

1.3 Trigonometric Functions and Their Inverses

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 x or y equals 1 or –1, the other coordinate equals zero, and r equals 1. To illustrate how to use this method to evaluate the trig values of 270°, first draw the figure below.