Answered: 5 cos x . XE %3! 13'

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 44RE

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Question

one of sin x, cos x, and tan x is given. Find the other
two if x lies in the specified interval.

Expert Solution

Step 1

Given that $\cos x = - \frac{5}{13} a n d x \in [\frac{π}{2}, π]$ .

This implies that,

$\begin{array}{rcl} \sin x & = & \sqrt{1 - \cos^{2} x} (∵ x l i e s i n Q I I) \\ = & \sqrt{1 - {(- \frac{5}{13})}^{2}} \\ = & \sqrt{1 - \frac{25}{169}} \\ = & \sqrt{\frac{169 - 25}{169}} \\ = & \sqrt{\frac{144}{169}} \\ = & \frac{12}{13} \end{array}$

Thus, $\begin{array}{rcl} \sin x & = & \frac{12}{13} \end{array}$ .

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