krete6a7

2023-02-27

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

Vincent Burke

$\mathrm{sec}x=\frac{1}{\mathrm{cos}x}$
$⇒\mathrm{sec}\left(\frac{\pi }{3}\right)=\frac{1}{\mathrm{cos}\left(\frac{\pi }{3}\right)}$
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,$⇒\mathrm{sec}\left(\frac{\pi }{3}\right)=\frac{1}{\frac{1}{2}}=2$

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