use a trigonometric identity to find the indicated value in the specified quadrant. Function Value sin θ = - 3/5 Quadrant IV Value cos θ

Solution

VerifiedGiven

$\sin \theta=-\frac{3}{5}$

Quadrant IV We need to find the value of $\cos \theta$ in the given quadrant.

Remember about the trigonometric identity

$\sin^2 \theta+\cos^2 \theta=1$

Therefore,

$\begin{align*} \sin^2 \theta+\cos^2 \theta&=1 &&\text{Subtract $\sin^2 \theta$ from both sides}\\ \cos^2 \theta&=1-\sin^2 \theta\\ \cos \theta&=\pm \sqrt{1-\sin^2 \theta} &&\text{In the Quadrant IV : $\cos \theta>0$}\\ \cos \theta&= \sqrt{1-\sin^2 \theta} &&\text{Substitute $\sin \theta=-\frac{3}{5}$}\\ \cos \theta&=\sqrt{1-\left(-\frac{3}{5}\right)^2}\\ \cos \theta&=\sqrt{1-\frac{9}{25}}\\ \cos \theta&=\sqrt{\frac{25-9}{25}}\\ \cos \theta&=\sqrt{\frac{16}{25}}\\ \cos \theta&=\frac{4}{5} \end{align*}$

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### enVision Algebra 1

1st Edition•ISBN: 9780328931576Al Cuoco, Christine D. Thomas, Danielle Kennedy, Eric Milou, Rose Mary Zbiek#### Big Ideas Math Integrated Mathematics II

1st Edition•ISBN: 9781680330687Boswell, Larson## More related questions

- college algebra
- college algebra

1/4

- college algebra
- college algebra

1/7