krete6a7

2023-02-27

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

Vincent Burke

Beginner2023-02-28Added 9 answers

$\mathrm{sec}x=\frac{1}{\mathrm{cos}x}$

$\Rightarrow \mathrm{sec}\left(\frac{\pi}{3}\right)=\frac{1}{\mathrm{cos}\left(\frac{\pi}{3}\right)}$

Using the $\frac{\pi}{3},\frac{\pi}{6},\frac{\pi}{2}\phantom{\rule{1ex}{0ex}}\text{triangle}\phantom{\rule{1ex}{0ex}}$

with sides of length 1 ,$\sqrt{3}\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}2$

We can determine $\mathrm{cos}\left(\frac{\pi}{3}\right)=\frac{1}{2}$ with accuracy.

Therefore,$\Rightarrow \mathrm{sec}\left(\frac{\pi}{3}\right)=\frac{1}{\frac{1}{2}}=2$

$\Rightarrow \mathrm{sec}\left(\frac{\pi}{3}\right)=\frac{1}{\mathrm{cos}\left(\frac{\pi}{3}\right)}$

Using the $\frac{\pi}{3},\frac{\pi}{6},\frac{\pi}{2}\phantom{\rule{1ex}{0ex}}\text{triangle}\phantom{\rule{1ex}{0ex}}$

with sides of length 1 ,$\sqrt{3}\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}2$

We can determine $\mathrm{cos}\left(\frac{\pi}{3}\right)=\frac{1}{2}$ with accuracy.

Therefore,$\Rightarrow \mathrm{sec}\left(\frac{\pi}{3}\right)=\frac{1}{\frac{1}{2}}=2$