Trigonometry · Grades 10 to 12
Radians and the unit circle
Convert angles and read exact values.
The idea
Radians measure angles with the radius as the unit. A full turn is 2π radians, which is 360 degrees.
Multiply degrees by π/180 to get radians. The unit circle gives the exact sine and cosine of common angles such as 30, 45 and 60 degrees.
Worked examples
- How to Convert Degrees to Radians Convert 135 degrees to radians in three steps. See the pi/180 factor, the simplification, and the factor mistakes to avoid.
- How to Evaluate sin 30 degrees on the Unit Circle Read sin 30 degrees from the unit circle. Three steps, the exact value, the axis-confusing mistakes to avoid and five practice questions.
- How to Convert Radians to Degrees Convert 5 pi/6 radians to degrees in three steps. Multiply by 180 over pi, cancel the pi, and avoid the conversion-factor mistakes.
Practice this topic
3 problems with answers.