trigonometry
I'm confused as to which quadrant $~+180^{\circ}~$ and $~+360^{\circ}~$ lie in.
If I'm able to determine this and their reference angles then I will be able to assign a positive or negative sign to the values of $~\cos 180^{\circ}~$ and $~\cos 360^{\circ}~$ .
Or is there another approach to this?
A slightly 'expanded-upon' version of user67418's answer:
The circle here represents the parametric curve $(x=\cos\theta, y=\sin\theta)$, and the line is the line $x+y=1$, so their points of intersection are the points where $\cos\theta+\sin\theta=1$; at least for me, this is the clearest way of seeing that there are only the two solutions already mentioned.
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.
Best Answer
Why not use the unit circle approach?
Since $180^{\circ}$ terminates in standard position at the point $(-1,0)$, $~\cos 180^{\circ}~ = -1$. Similarly, $~\cos 360^{\circ}~ = 1$ as $360^{\circ}$ terminates at $(1,0)$ in standard position.