Chapter 7: Q. 4 (page 485)

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

Short Answer

Expert verified

$\cos α = - \frac{3}{5}$

Step by step solution

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculate the adjacent side

Step 3. Find cos α

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ifsinα=-45,π<α<3π2, thencosα=_____

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

Pure Maths

Statistics

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Study anywhere. Anytime. Across all devices.

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