Question

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

Answer 1

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