# If sec(t) = 3, how do you find the exact value of cos(t)?

May 14, 2018

$\cos \left(t\right) = \frac{1}{3}$

#### Explanation:

Since $\sec \left(t\right) = \frac{1}{\cos} \left(t\right)$, you have

$\sec \left(t\right) = 3 \setminus \iff \frac{1}{\cos} \left(t\right) = 3 \setminus \iff \cos \left(t\right) = \frac{1}{3}$

The first step used the definition of the secant function, rewriting it as the inverse of the cosine function, while in the second step we inverted both sides, using the relation

$a = b \setminus \implies \frac{1}{a} = \frac{1}{b}$