Question

PART B:What are the exact values of all six trigonometric functions evaluated at θ?

Answer 1

Adding 4pi to theta, we can find a coterminal angle between 0 and 2pi:

`-(11)/(4)\pi+4\pi=-(11)/(4)\pi+(16)/(4)\pi=(5)/(4)\pi`

This new angle is in quadrant III, so the sine and cosine relations are negative.

Calculating all trigonometric functions of this angle, we have:

`\begin{gathered} \sin ((5)/(4)\pi)=-\frac{\sqrt[]{2}}{2} \\ \cos ((5)/(4)\pi)=-\frac{\sqrt[]{2}}{2} \\ \tan ((5)/(4)\pi)=(\sin ((5)/(4)\pi))/(\cos ((5)/(4)\pi))=1 \\ \csc ((5)/(4)\pi)=(1)/(\sin((5)/(4)\pi))=-\sqrt[]{2} \\ \sec ((5)/(4)\pi)=(1)/(\cos((5)/(4)\pi))=-\sqrt[]{2} \\ \cot ((5)/(4)\pi)=(1)/(\tan ((5)/(4)\pi))=1 \end{gathered}`