Question

What is the value of $\cos 180°$?

Answer 1

Find the value of $\cos 180°$.

$\begin{array}{rcl}\cos 180°& =& \cos \left(90°+90°\right)\\ & \Rightarrow & \cos 180°=\cos 90°\cos 90°-\sin 90°\sin 90°\left\{\because \cos \left(A+B\right)=\cos A\cos B-\sin A\sin B\right\}\\ & \Rightarrow & \cos 180°=0-1\left\{\because \cos 90°=0,\sin 90°=1\right\}\\ & \Rightarrow & \cos 180°=-1\end{array}$

Hence, the required value is$\begin{array}{l}\cos 180°\end{array}=-1$.