Try the fastest way to create flashcards
Question

# 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

Verified
Step 1
1 of 2

Given

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

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

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

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*}

## Recommended textbook solutions

#### enVision Algebra 1

1st EditionISBN: 9780328931576Al Cuoco, Christine D. Thomas, Danielle Kennedy, Eric Milou, Rose Mary Zbiek
3,653 solutions

#### Precalculus with Limits

3rd EditionISBN: 9781133962885 (3 more)Larson
11,068 solutions

#### Algebra 1

4th EditionISBN: 9781602773011Saxon
5,377 solutions

#### Big Ideas Math Integrated Mathematics II

1st EditionISBN: 9781680330687Boswell, Larson
4,539 solutions