This is question 1c of a list of related items.
State the value(s) of $\theta$ in the range $0^\circ$ to $360^\circ$ so that the following is true:
$$\tan\theta = \tan 20^\circ$$
Here is the answer (from the list of answers):
$$\theta = 20^\circ;\quad \theta=180^\circ+20^\circ=200^\circ$$
I am using the trig identity for tan, the one where
$$\tan\theta = \tan(\theta-180^\circ)$$
If $\theta = 20^\circ$ for the question, then $\tan(\theta-180^\circ)$ is $\tan(20^\circ-180^\circ)$, which is $\tan(-160^\circ)$, which is taking me to a completely different direction than the solution.
I would appreciate it if someone could explain the steps of using this trig identity to determine which other angles have the same tan ratio as $20^\circ$.
Best Answer
Hint:period of tangent function is $180^\circ, \tan 20^\circ=\tan(180+20)^\circ, \tan(20-180)^\circ =\tan(-160)^\circ, 200^\circ$ is anticlockwise rotation, $-160^\circ$ is clockwise rotation.