The sine of theta is the y-value divided by the distance from the origin.
The cosine of theta is the x-value divided by the distance from the origin.
This applet reduces the distance of (x, y) from the origin to 1. Due to triangle symmetry, the length on the x-axis is the cosine ratio, and the length on the y-axis is the sine ratio.
Click on the play button in the lower left to automatic the applet.

Do the cos θ and the sin θ have a maximum value?
In which quadrants is cos θ negative? positive?
In which quadrants is sin θ negative? positive?