Question

How do you evaluate $\sec \left(\frac{\mathrm{\pi }}{3}\right)$?

Answer 1

Find the value of $\sec \left(\frac{\mathrm{\pi }}{3}\right)$:

The given expression is $\sec \left(\frac{\mathrm{\pi }}{3}\right)$.

Use the trigonometric identities to obtain the value of $\sec \left(\frac{\mathrm{\pi }}{3}\right)$

$\begin{array}{rcl}\sec \left(\frac{\mathrm{\pi }}{3}\right)& =& \frac{1}{\cos \left(\frac{\mathrm{\pi }}{3}\right)}\left[\because \sec \left(x\right)=\frac{1}{\cos \left(x\right)}\right]\\ & \Rightarrow & \sec \left(\frac{\mathrm{\pi }}{3}\right)=\frac{1}{{\displaystyle \frac{1}{2}}}\left[\because \cos \left(\frac{\mathrm{\pi }}{3}\right)=\frac{1}{2}\right]\\ \therefore \sec \left(\frac{\mathrm{\pi }}{3}\right)& =& 2\end{array}$

Hence, the value of $\sec \left(\frac{\mathrm{\pi }}{3}\right)=2$.