Question

Sin(−θ)=1/5 and tanθ=√6/12 What is the value of cosθ ?

Answer 1

$\bf sin(-\theta)\iff -sin(\theta)\qquad \qquad tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\\\\ -----------------------------\\\\ tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\implies cos(\theta)=\cfrac{sin(\theta)}{tan(\theta)}\quad \begin{cases} sin(-\theta)=\cfrac{1}{5}\\\\ -sin(\theta)=\cfrac{1}{5}\\\\ sin(\theta)=-\cfrac{1}{5}\\ --------\\ tan(\theta)=\cfrac{\sqrt{6}}{12} \end{cases} \\\\\\ thus\qquad cos(\theta)=\cfrac{-\frac{1}{5}}{\frac{\sqrt{6}}{12}}$

simplify away