Question

Find the value of each trig function. 1. sec 225°2. csc 3pi/43. tan 5pi/4

Answer 1

The value of:

$\begin{gathered} \sec (225^{\circ})=-\sqrt[]{2}=-1.414 \\ \sec (225^{\circ})=\frac{1}{\cos (225^{\circ})} \\ \sec (225^{\circ})=\frac{1}{\cos (180+45)} \\ \sec (225^{\circ})=\frac{1}{\cos (180)\cos (45)-\sin (180)\sin (45)} \\ \sec (225^{\circ})=\frac{1}{-1\times\frac{1}{\sqrt[]{2}}-0\times\frac{1}{\sqrt[]{2}}} \\ \sec (225^{\circ})=-\sqrt[]{2} \end{gathered}$

And

$\csc (\frac{3\pi}{4})=\sqrt[]{2}=1.414$

And:

$\tan (\frac{5\pi}{4})=1$