What is the exact value of $\mathrm{sec}-330$?

Aydin Jarvis
2022-10-15
Answered

What is the exact value of $\mathrm{sec}-330$?

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na1p1a2pafr

Answered 2022-10-16
Author has **16** answers

$\mathrm{sec}(-330)$

-330 will be in the first quadrant

-330=+30

$\therefore \mathrm{sec}(-330)=\mathrm{sec}30$

$\mathrm{sec}30=\frac{1}{\mathrm{cos}30}$

$\because \mathrm{cos}30=\frac{\sqrt{3}}{2}$

$\mathrm{sec}30=\frac{1}{\frac{\sqrt{3}}{2}}=\frac{2}{\sqrt{3}}$

rationalising

$\mathrm{sec}30=\frac{2\sqrt{3}}{3}$

-330 will be in the first quadrant

-330=+30

$\therefore \mathrm{sec}(-330)=\mathrm{sec}30$

$\mathrm{sec}30=\frac{1}{\mathrm{cos}30}$

$\because \mathrm{cos}30=\frac{\sqrt{3}}{2}$

$\mathrm{sec}30=\frac{1}{\frac{\sqrt{3}}{2}}=\frac{2}{\sqrt{3}}$

rationalising

$\mathrm{sec}30=\frac{2\sqrt{3}}{3}$

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