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 tan x = sin x cos x ; where cos x ≠ 0 . Calculation: The value of the given expression tan ( 150 ° ) is evaluated as follows. By the above definition, the expression can be rewritten as tan ( 150 ° ) = sin ( 150 ° ) cos ( 150 ° ) . The terminal side of an angle of degree measure 150 passes through the point A ( − 3 2 , 1 2 ) on the unit circle as shown below in Figure 2. From Figure 2, the x -coordinate of the point A is cos ( 150 ° ) = − 3 2 and the y -coordinate of the point A is sin ( 150 ° ) = 1 2

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

15th Edition

ISBN: 9781323047620

Author: Barnett, Ziegler, Byleen

Publisher: Pearson Education

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Chapter 8.2, Problem 39E

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To find: The exact value of tan(150°) without the use of a calculator.

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Chapter 8.2, Problem 38E

Chapter 8.2, Problem 40E

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Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

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The exact value of tan ( 150 ° ) without the use of a calculator.

Solution Summary: The author explains how to find the exact value of mathrmtan(150°) without the use of a calculator.

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