Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Recall what the relationship between cosine and secant:

$\sec(\theta)=\frac{1}{\cos(\theta)}$

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:

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

Then secant must be:

$\sec(\theta)=\frac{5}{4}$

So:

$\sec^2(\theta)=(\frac{5}{4})^2$

Square:

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

And we're done!