Question

How do you evaluate $\sec \left(150°\right)$ ?

Answer 1

Compute the required value.

We know that, $\sec \left(180°-\theta \right)=-\sec \left(\theta \right)$.

$150$ can be written as $180-30$.

Thus, $\sec \left(150°\right)=\sec \left(180°-30°\right)$

$$\begin{gathered} =-\sec \left(30°\right) \\ =-\frac{2}{\sqrt{3}} \end{gathered}$$

Hence, the value of $\sec \left(150°\right)$ is $-\frac{2}{\sqrt{3}}$.