TABLE OF CONTENTS The trigonometric function values for some common angles should be committed to memory. Consider the 30-60-90 and 45-45-90 degree triangles shown in Figures 20.54A and 20.54B.
By looking at Figure 20.54A and Figure 20.54B we can readily find the values of the six trigonometric functions for 30, 60, and 45 degrees and generate the entries for Table 20.5.
| Relationship | 30 | 45 | 60 | |
|---|---|---|---|---|
| sin | opp/hyp | 1/2 | | |
| cos | adj/hyp | | | 1/2 |
| tan | opp/adj | | 1/1 = 1 | |
| cot | adj/opp | | 1/1 = 1 | |
| sec | hyp/adj | | | 2/1 = 2 |
| csc | hyp/opp | 2/1 = 2 | | |
by multiplying the ratio like this:
Likewise,
The trigonometric function values for 0 and 90 degrees are more abstract. To visualize the trigonometric functions for these angles we draw imaginary right triangles in which one side has a length of 0. The triangle for 0 degrees is shown in Figure 20.55.
From Figure 20.55 we can calculate the trigonometric function values of 0 degrees as shown.
? is the symbol for undefined.
The triangle shown in Figure 20.56 shows the imaginary triangle used to find the values for the trigonometric functions of 90 degrees.
From Figure 20.56 we can calculate the trigonometric...
