Question

Given sin(−θ)= −1/4 and tanθ= 15√15 . What is the value of cosθ ?

Answer 1

$\sin = \frac{y}{r} \\ \\ \tan = \frac{y}{x} \\ \\ \cos = \frac{x}{r} \\ \\ {x}^{2} + {y}^{2} = {r}^{2}$

$- \sin = \frac{ - 1 \: = \: y}{4 \: = \: r}$
$15 \sqrt{15} = \frac{1}{x} \\ \\ x = .017$
$\cos = \frac{.017}{4} = .0043$