Question

Evaluate without using a calculator by using ratios in a reference triangle sec 3pi/4

Answer 1

`\bf sec\left( (3\pi )/(4) \right)\implies \cfrac{1}{cos\left( (3\pi )/(4) \right)}\implies \cfrac{1}{-(√(2))/(2)}\implies -\cfrac{2}{√(2)} \\\\\\ \textit{now, let's rationalize the denominator} \\\\\\ -\cfrac{2}{√(2)}\cdot \cfrac{√(2)}{√(2)}\implies -\cfrac{2√(2)}{2}\implies \boxed{-√(2)}`