Question

Find the exact values of $\cos 150°$ and $\sin 150°$.

Answer 1

Step 1: Compute the exact value of $\cos 150°$:

Since, $150°=180°-30°$

So we can write $\cos 150°$ as

$$\begin{gathered} \cos 150°=\cos \left(180°-30°\right) \\ =-\cos 30° \end{gathered}$$ $\left[\because \cos (180-\theta )=-\cos \theta \right]$

$=-\frac{\sqrt{3}}{2}\left[\because \cos 30°=\frac{\sqrt{3}}{2}\right]$

Step 2: Compute the exact value of $\sin 150°$:

We can find the value as

$\sin 150°=\sin \left(180°-30°\right)$

$=\sin 30°\left[\because \sin \left(180-\theta \right)=\sin \theta \right]$

$=\frac{1}{2}\left[\because \sin 30°=\frac{1}{2}\right]$

Hence, the exact value of $\cos 150°=-\frac{\sqrt{3}}{2}$ and $\sin 150°=\frac{1}{2}$.