Common Radian Angles

Definition

Common radian angles are standard unit-circle landmarks used for exact trig values.

They serve as the essential reference points for navigating trigonometry without relying on a calculator for every step.

$30^\circ=\pi/6$ $3 0^{\circ} = π /6$ , $45^\circ=\pi/4$ $4 5^{\circ} = π /4$ , $60^\circ=\pi/3$ $6 0^{\circ} = π /3$ , $90^\circ=\pi/2$ $9 0^{\circ} = π /2$ , $180^\circ=\pi$ $18 0^{\circ} = π$ , and $360^\circ=2\pi$ $36 0^{\circ} = 2 π$ .
- How to read: “Thirty degrees equals pi over six, forty five degrees equals pi over four, sixty degrees equals pi over three, ninety degrees equals pi over two, one hundred eighty degrees equals pi, and three hundred sixty degrees equals two pi.”
- Meaning / when to use: Memorize these degree–radian pairs for exact sine, cosine, and tangent values on the unit circle without a calculator.
This concept is part of the chapter-by-chapter synthesis from Trigonometry For Dummies.
It should be merged with existing math notes if a stronger canonical note already exists.