Question

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

Answer 1

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