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, and the axis-confusing mistakes to avoid.
- How to Find a Missing Side with Sine Find the opposite side when the angle is 30 degrees and the hypotenuse is 12. Four steps with SOH CAH TOA and the mistakes to avoid.
Practice this topic
3 problems with answers.