Question

What is the value of $\cos (120°)$?

Answer 1

Find the value of $\cos \left(120°\right)$.

$\begin{array}{rcl}\cos \left(120°\right)& =& \cos \left(90°+30°\right)\\ & \Rightarrow & \cos \left(120°\right)=-\sin \left(30°\right)\left\{\because cos\left(90°+\theta \right)=-sin\left(\theta \right)\right\}\\ & \Rightarrow & \cos \left(120°\right)=-\frac{1}{2}\left\{\because sin\left(30°\right)=\frac{1}{2}\right\}\end{array}$

Hence, the required value is $\begin{array}{l}\cos \left(120°\right)\end{array}=-\frac{1}{2}$