Chapter 7: Q. 2 (page 485)

if $\sin θ = \frac{4}{5}$ and $θ$ is in quadrant 2, then $\cos θ =$ ______

Short Answer

Expert verified

$\cos θ = - \frac{3}{5}$

Step by step solution

Step 1. Given information

We have been given the value of $\sin θ$ which is $\frac{4}{5}$ and $θ$ is in second quadrant.

We have to find the value of $\cos θ$

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

role="math" localid="1646455498886" $\sin θ = \frac{4}{5} : \frac{o p p o s i t e}{h y p o t e n u s e}$

Calculate the adjacent side,

role="math" localid="1646455604923" $a d j a c e n t = \sqrt{h y p o t e n u s e^{2} - o p p o s i t e^{2}} = \sqrt{25 - 16} = \sqrt{9} = 3$

Step 3. Find the value of cos θ

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

and $\cos (θ)$ is negative in the second quadrant.

Thus,

localid="1646455781307" $\cos θ = - \frac{3}{5}$

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if $\sin θ = \frac{4}{5}$ and $θ$ is in quadrant 2, then $\cos θ =$ ______

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculate the adjacent side

Step 3. Find the value of cos θ

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if sinθ=45and θis in quadrant 2, thencosθ=______

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculate the adjacent side

Step 3. Find the value of cos θ

One App. One Place for Learning.

Most popular questions from this chapter

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if $\sin θ = \frac{4}{5}$ and $θ$ is in quadrant 2, then $\cos θ =$ ______