Question

If costheta=4/5 then what is sec^2theta

Answer 1

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

Explanation:

Recall what the relationship between cosine and secant:

`\sec(\theta)=(1)/(\cos(\theta))`

In other words, secant is the reciprocal of cosine.

So, if we know cosine, we only need to find its reciprocal to find secant.

We are given that cosine is:

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

Then secant must be:

`\sec(\theta)=(5)/(4)`

So:

`\sec^2(\theta)=((5)/(4))^2`

Square:

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

And we're done!