**Problem Statement**Find the exact values of $ s $ in the given interval that satisfy the given condition:\[[0, 2\pi); \quad \cos s = -\frac{\sqrt{2}}{2}\]

We have given cos s=-22, where s∈[0,2π) We know that cosθis negative in quadrant II and quadrant…

Answered: **Problem Statement** Find the exact…

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Related questions

Question

**Problem Statement**

Find the exact values of $ s $ in the given interval that satisfy the given condition:

\[
[0, 2\pi); \quad \cos s = -\frac{\sqrt{2}}{2}
\]

Expert Solution

Step 1

We have given $\cos s = - \frac{\sqrt{2}}{2}$ , where $s \in [0, 2 π)$

We know that $\cos θ$ is negative in quadrant II and quadrant III.

Therefore, here $s$ will lies in quadrant II and quadrant III.

Now,

$\begin{array}{rcl} \cos s & = & - \frac{\sqrt{2}}{2} \\ s & = & \cos^{- 1} (- \frac{\sqrt{2}}{2}) \\ s & = & \cos^{- 1} (\frac{\sqrt{2}}{2}) (S i n c e \cos^{- 1} (- x) = \cos^{- 1} (x)) \\ s & = & \cos^{- 1} (\cos \frac{π}{4}) (S i n c e \cos \frac{π}{4} = \frac{\sqrt{2}}{2}) \\ s & = & \frac{π}{4} \end{array}$