Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 4 (page 485)

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

Short Answer

Expert verified

$\cos 伪 = - \frac{3}{5}$

Step by step solution

Step 1. Given information

Given is:

$\sin 伪 = - \frac{4}{5}$

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

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 $胃$ be the angle formed by the intersection of the adjacent and the hypotenuse sides. We get

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

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

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

Therefore,

$\cos 伪 = - \frac{3}{5}$

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91影视

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculate the adjacent side

Step 3. Find cos α

One App. One Place for Learning.

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91影视

ifsin伪=-45,蟺<伪<3蟺2, thencos伪=_____

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculate the adjacent side

Step 3. Find cos α

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Statistics

Discrete Mathematics

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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