530 CHAPTER 5 Trigonometric Functions (b) Add 360° to the given negative angle measure to obtain the angle of least positive measure. See Figure 12. -75° + 360° = 285° (c) The least integer multiple of 360° greater than 800° is 3 # 360° = 1080°. Add 1080° to -800° to obtain -800° + 1080° = 280°. S Now Try Exercises 81, 91, and 95. EXAMPLE 5 Finding Measures of Coterminal Angles Find the angle of least positive measure that is coterminal with each angle. (a) 908° (b) -75° (c) -800° SOLUTION (a) Subtract 360° as many times as needed to obtain an angle with measure greater than 0° but less than 360°. 908° - 2 # 360° = 188° Multiply 2 # 360°. Then subtract. An angle of 188° is coterminal with an angle of 908°. See Figure 11. 0 x y 188° 908° Figure 11 0 285° –75° x y Figure 12 Examples of Angles Coterminal with 60° Value of n Angle Coterminal with 60° 2 60° + 2 # 360° = 780° 1 60° + 1 # 360° = 420° 0 60° + 0 # 360° = 60° (the angle itself) -1 60° + 1-12 # 360° = -300° -2 60° + 1-22 # 360° = -660° Sometimes it is necessary to find an expression that will generate all angles coterminal with a given angle. For example, we can obtain any angle coterminal with 60° by adding an integer multiple of 360° to 60°. Let n represent any integer. Then the following expression represents all such coterminal angles. 60° + n # 360° Angles coterminal with 60° The table below shows a few possibilities.
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