Chapter 3 - Section 3.9 - Inverse Trigonometric Functions - Exercises - Page 181: 12

$-\frac{\sqrt 3}{3}$

Work Step by Step

The given problem can be solved as: $cot({sin^{-1}(-\frac{\sqrt 3}{2})})=cot ( -\frac{\pi}{3})$ or, $cot ( -\frac{\pi}{3})=\frac{-\sqrt 3}{3}$ Hence. the final answer is: $-\frac{\sqrt 3}{3}$

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