Question

Fill in the blank.if necessary, use the slash marks (/) for a function bar. if sin theta= 3/5, then cos theta=

Answer 1

Answer:

4/5 or -4/5

Step-by-step explanation:

We are going to use the Pythagorean Identity:

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

We are given the value of $\sin(\theta)$ which is 3/5 so plug that in:

$(\frac{3}{5})^2+\cos^2(\theta)=1$

Simplify:

$\frac{9}{25}+\cos^2(theta)=1$

Subtract 9/25 on both sides:

$\cos^2(\theta)=1-\frac{9}{25}$

$\cos^2(\theta)=\frac{16}{25}$

Take the square root of both sides:

$\cos(\theta)=\pm \sqrt{\frac{16}{25}}$

$\cos(\theta)=\pm \frac{4}{5}$