Question

If sin theta =7/25, use the Pythagorean identity to find cos theta

Answer 1

`\cos(\theta)=\pm (24)/(25)`

Explanation:

I don't know where
`\theta` is so there is going to be two possibilities for cosine value, one being positive while the other is negative.

A Pythagorean Identity is
`\cos^2(\theta)+\sin^2(\theta)=1`.

We are given
`\sin(\theta)=(7)/(25)`.

So we are going to input
`(7)/(25)` for the
`sin(\theta)`:

`\cos^2(\theta)+((7)/(25))^2=1`

`\cos^2(\theta)+(49)/(625)=1`

Subtract 49/625 on both sides:

`\cos^2(\theta)=1-(49)/(625)`

Find a common denominator:

`\cos^2(\theta)=(625-49)/(625)`

`\cos^2(\theta)=(576)/(625)`

Square root both sides:

`\cos(\theta)=\pm \sqrt{(576)/(625)}`

`\cos(\theta)=\pm (√(576))/(√(625))`

`\cos(\theta)=\pm (24)/(25)`