Question

PLEASE can someone explain why The exact value of sec ( π/6) is 2 /√ 3 ??

Answer 1

$\bf sec\left( \frac{\pi }{6} \right)\qquad recall\to sec(\theta)=\cfrac{1}{cos(\theta)}\qquad thus \\\\ sec\left( \frac{\pi }{6}\right)\iff \cfrac{1}{cos\left( \frac{\pi }{6}\right)} \\\\\\ \textit{check your Unit Circle for what the }cos\left( \frac{\pi }{6}\right)\ is \\\\\\ \cfrac{1}{\frac{\sqrt{3}}{2}}\implies \cfrac{\frac{1}{1}}{\frac{\sqrt{3}}{2}}\implies \cfrac{1}{1}\cdot \cfrac{2}{\sqrt{3}}\implies \cfrac{2}{\sqrt{3}}$