553 5.3 Trigonometric Function Values and Angle Measures CAUTION A common error is to find the reference angle by using the terminal side of u and the y-axis. The reference angle is always found with reference to the x-axis. 0 x y 388 2188 2188 – 1808 = 388 (a) 0 x y 538 3078 3608 – 3078 = 538 (b) Figure 34 EXAMPLE 4 Finding Reference Angles Find the reference angle for each angle. (a) 218° (b) 1387° SOLUTION (a) As shown in Figure 34(a), the positive acute angle made by the terminal side of this angle and the x-axis is 218° - 180° = 38°. For u = 218°, the reference angle u′ = 38°. Figure 33 x y O u in quadrant II u u9 x y u in quadrant III O u u9 u in quadrant IV x y O u u9 (b) First find a coterminal angle between 0° and 360°. Divide 1387° by 360° to obtain a quotient of about 3.9. Begin by subtracting 360° three times (because of the whole number 3 in 3.9). 1387° - 3 # 360° = 1387° - 1080° Multiply. = 307° Subtract. The reference angle for 307° (and thus for 1387°) is 360° - 307° = 53°. See Figure 34(b). S Now Try Exercises 57 and 61.
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