Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

if $\sin α = - \frac{4}{5}$ , $π < α < \frac{3 π}{2}$ , then $\cos α =$ _____

$\cos α = - \frac{3}{5}$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

Given is:

$\sin α = - \frac{4}{5}$

We have to find the value of $\cos α$ .

Step 2. Calculate the adjacent side

We consider the right-angled triangle which opposite side is equal to $- 4$ and its hypotenuse equals to $5$ and let $θ$ be the angle formed by the intersection of the adjacent and the hypotenuse sides. We get

$\sin α = - \frac{4}{5} : \frac{o p p o s i t e}{h y p o t e n u s e}$

Calculate the adjacent side,

$a d j a c e n t = \sqrt{h y p o t e n u s e^{2} - o p p o s i t e^{2}} = \sqrt{25 - 16} = \sqrt{9} = 3$

Step 3. Find cos α

As $\cos α = \frac{a d j a c e n t}{h y p o t e n u s e}$

and $\cos α$ is negative in the second quadrant.

Therefore,

$\cos α = - \frac{3}{5}$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

if $\sin α = - \frac{4}{5}$ , $π < α < \frac{3 π}{2}$ , then $\cos α =$ _____

Step by Step Solution

Step 1. Given information

Step 2. Calculate the adjacent side

Step 3. Find cos α

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Step by Step Solution

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if $\sin α = - \frac{4}{5}$ , $π < α < \frac{3 π}{2}$ , then $\cos α =$ _____