Skill: Convert between degrees and radians

Degree–radian conversion rests on the fact that a full rotation is $360^\circ=2\pi$ radians, so $180^\circ=\pi$ radians; measures are converted by multiplying by $\pi/180$ or $180/\pi$. Radians represent the ratio of an arc’s length to the circle’s radius, supporting exact angle representations such as $30^\circ=\pi/6$ and $3\pi/4=135^\circ$ for trigonometric functions and graphs. Radian-based calculus formulas and more advanced applications are not included.