Question

How do you find the values of $\theta$ given $\tan \theta =1$ ?

Answer 1

Explanation:
$\tan \theta =1$
You then do inverse tan to find what it is in degrees or radians:
$\theta ={\tan }^{-1}\left(1\right)={45}^o$ or $\frac{\pi }{4}$

On the tan graph the point 1 is repeated but at a different angle so you add ${180}^o$ to ${45}^o$ since it is positive. You use the 'CAST' diagram:

C- cosine is positive so you do ${360}^o$ - angle (angle you calculated)

A- all are positive

S- sine is positive so you do ${180}^o$ - angle

T- tan is positive so you do ${180}^o$ + angle

$180+45=225$ degrees or $3.93$ rad