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

4/5 or -4/5

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:

`((3)/(5))^2+\cos^2(\theta)=1`

Simplify:

`(9)/(25)+\cos^2(theta)=1`

Subtract 9/25 on both sides:

`\cos^2(\theta)=1-(9)/(25)`

`\cos^2(\theta)=(16)/(25)`

Take the square root of both sides:

`\cos(\theta)=\pm \sqrt{(16)/(25)}`

`\cos(\theta)=\pm (4)/(5)`