Chapter 1 | Functions and Graphs
65
Figure 1.32 For a point P = ( x , y ) on a circle of radius r , the coordinates x and y satisfy x = r cos θ and y = r sin θ .
Table 1.9 shows the values of sine and cosine at the major angles in the first quadrant. From this table, we can determine the values of sine and cosine at the corresponding angles in the other quadrants. The values of the other trigonometric functions are calculated easily from the values of sin θ and cos θ . θ sin θ cos θ
0
0
1
π 6
1 2
3
2
π 4
2
2
2
2
π 3
1 2
3
2
π 2
0
1
Table 1.9 Values of sin θ and cos θ at Major Angles θ in the First Quadrant
Example 1.23 Evaluating Trigonometric Functions Evaluate each of the following expressions. a. sin ⎛ ⎝ 2 π 3 ⎞ ⎠
⎛ ⎝ − 5 π 6
⎞ ⎠
b. cos
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