Question : What is the value of $\sec 330°$?
Option 1: $2$
Option 2: $\frac{–2}{\sqrt3}$
Option 3: $–2$
Option 4: $\frac{2}{\sqrt3}$
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Correct Answer: $\frac{2}{\sqrt3}$
Solution :
Use the trigonometric identity,
$\sec (360°-\theta)=\operatorname{sec} \theta$
The value of $\sec 330°$ is given as,
$\sec 330°= \sec(360°- 30°)$
⇒ $\sec 330°= \operatorname{sec} 30°$
⇒ $\operatorname{sec} 30°=\frac{2}{\sqrt3}$
⇒ $\sec 330°= \frac{2}{\sqrt3}$
Hence, the correct answer is $\frac{2}{\sqrt3}$.
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