Question

I just took a test and my brain is fried please help thanks

Answer 1

`tan(\theta )=√(3)\implies tan(\theta )=\cfrac{√(3)}{1}\implies tan(\theta )=\cfrac{√(3)}{1}\cdot \cfrac{2}{2} \implies tan(\theta )=\cfrac{√(3)}{2}\cdot \cfrac{2}{1} \\\\\\ tan(\theta )=\cfrac{~~\stackrel{sin(\theta )}{(√(3))/(2)} ~~}{\underset{cos(\theta )}{(1)/(2)}}\implies \theta =tan^(-1)\left( \cfrac{~~(√(3))/(2) ~~}{(1)/(2)} \right)\implies \theta = \begin{cases} \stackrel{I~Quadrant}{60^o}\\\\ \stackrel{III~Quadrant}{240^o} \end{cases}`

Check the picture below.