# If sec(t) = 3, how do you find the exact value of sin^2 (t)?

Nov 27, 2015

Find ${\sin}^{2} t$
Ans: ${\sin}^{2} t = \frac{8}{9}$
$\sec t = \frac{1}{\cos t} = 3$ --> $\cos t = \frac{1}{3}$ --> ${\cos}^{2} t = \frac{1}{9}$
${\sin}^{2} t = 1 - {\cos}^{2} t = 1 - \frac{1}{9} = \frac{9}{9} - \frac{1}{9} = \frac{8}{9}$