Let an angle whose measure in radians is $\theta$ be placed onto the Cartesian plane such that one of its rays $R_1$ corresponds to the nonnegative $x$ axis and one can go from the point $(1,0)$ to the point that is the intersection of the other ray $R_2$ of the angle with the circle $x^2+y^2=1$ by traveling exactly $\theta$ units on the circle. (If $\theta$ is positive, the distance should be traveled counterclockwise; otherwise, the distance $|\theta|$ should be traveled clockwise. Also, note that ``other ray'' is used quite loosely, as it may also correspond to the nonnegative $x$ axis also.) Then $R_2$ is the terminal ray of the angle.

The picture below shows the terminal ray $R_2$ of the angle $\displaystyle \theta=\frac{2\pi}{3}$ .