Answer
$tan\theta=\sqrt 3$
$sin \theta=\frac{\sqrt 3}{2}$
$sec\theta=2$
$csc\theta=\frac{2\sqrt 3}{3}$
$cot\theta==\frac{\sqrt 3}{3}$
Work Step by Step
$ cos\theta=1/2$ I quadrant
All other five trig functions are positive beacause cos is in the I quadrant
$sin \theta=\sqrt {1-(\frac{1}{2}^{2})} $ Use the trig identity $cos \theta^2+sin \theta^2=1$
$sin \theta=\sqrt {1-\frac{1}{4}} =\sqrt \frac{3}{4}=\frac{\sqrt 3}{2}$
$tan\theta=\frac{sin\theta}{cos\theta}=\sqrt 3$
$sec\theta=\frac{1}{cos\theta}=2$
$csc\theta=\frac{1}{sin\theta}=\frac{2}{\sqrt 3}=\frac{2}{\sqrt 3}\frac{\sqrt 3}{\sqrt 3}=\frac{2\sqrt 3}{3}$
$cot\theta=\frac{1}{tan\theta}=\frac{1}{\sqrt 3}=\frac{\sqrt 3}{3}$
