# Question 2daa7

Aug 15, 2017

$\text{see explanation}$

#### Explanation:

$\cos \theta < 0$ indicating that $\theta$ could be in the second or third quadrants.

•color(white)(x)sin^2theta+cos^2theta=1

$\Rightarrow \sin \theta = \pm \sqrt{1 - {\cos}^{2} \theta}$

$\textcolor{w h i t e}{\Rightarrow \sin \theta} = \pm \sqrt{1 - {\left(- \frac{1}{2}\right)}^{2}}$

$\textcolor{w h i t e}{\Rightarrow \sin \theta} = \pm \sqrt{\frac{3}{4}} = \pm \frac{\sqrt{3}}{2}$

•color(white)(x)tantheta=sintheta/costheta=+-(sqrt3/2)/(1/2)=+-sqrt3

•color(white)(x)cottheta=1/tantheta=+-1/sqrt3

•color(white)(x)sectheta=1/costheta=1/(-1/2)=-2

•color(white)(x)csctheta=1/sintheta=+-1/(sqrt3/2)=+-2/sqrt3#