Answer:
[tex]\sec^2(\theta)=\frac{25}{16}[/tex]
Step-by-step explanation:
Recall what the relationship between cosine and secant:
[tex]\sec(\theta)=\frac{1}{\cos(\theta)}[/tex]
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:
[tex]\cos(\theta)=\frac{4}{5}[/tex]
Then secant must be:
[tex]\sec(\theta)=\frac{5}{4}[/tex]
So:
[tex]\sec^2(\theta)=(\frac{5}{4})^2[/tex]
Square:
[tex]\sec^2(\theta)=\frac{25}{16}[/tex]
And we're done!
