cdcamandokwd

2022-12-01

What is the exact value of $\mathrm{sec}\left(\frac{\pi }{4}\right)$?

greffhc

Expert

Identify the value of$\mathrm{sec}\left(\frac{\pi }{4}\right)$:
We know that $\mathrm{sec}\theta =\frac{1}{\mathrm{cos}\theta }$.
Using the aforementioned property, we get
$\mathrm{sec}\left(\frac{\pi }{4}\right)=\frac{1}{\mathrm{cos}\left(\frac{\pi }{4}\right)}$
$⇒$$\mathrm{sec}\left(\frac{\pi }{4}\right)=\frac{1}{\frac{1}{2}}$$\left(\because \mathrm{cos}\left(\frac{\pi }{4}\right)=\frac{1}{2}\right)$
$⇒$$\mathrm{sec}\left(\frac{\pi }{4}\right)=2$
Hence, the exact value of $\mathrm{sec}\left(\frac{\pi }{4}\right)$ is $2$.

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