Explanation Definition used: 1. Let x be the radian measure of an angle in standard position, and let P = ( a , b ) be the point on the unit circle that lies on the terminal side of the angle in Figure 1. Then sin x = b and cos x = a . 2. The trigonometric function csc x = 1 sin x ; where sin x ≠ 0 . Calculation: The value of the given expression csc π 3 is evaluated as follows. By the above definition, the expression can be rewritten as csc π 3 = 1 sin π 3 . The terminal side of an angle of radian measure π 3 ( 60 ° ) passes through the point A ( 1 2 , 3 2 ) on the unit circle as shown below in Figure 2

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The exact value of the expression csc π 3 without the use of a calculator.

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