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

1 answer:

7 0

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

simplify away

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To start things off, you must put everything on the opposite side of y so that you only have the y variable left.

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