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MATH GUIDE · TRIGONOMETRY

Degrees vs. radians on a calculator

Angle mode is one of the most common reasons a trigonometric result differs from an expected answer.

What are degrees?

Degrees divide a full rotation into 360 equal parts. A right angle is 90°, and a straight angle is 180°. Many introductory geometry problems express angles in degrees.

What are radians?

Radians measure an angle using the relationship between arc length and radius. A full rotation is 2π radians, a straight angle is π radians, and a right angle is π/2 radians. Radians are especially common in algebra, precalculus, and calculus.

Why does angle mode matter?

The numerical input to sine, cosine, and tangent is interpreted according to the active angle unit. For example, sin(30°) is 0.5, while sin(30 radians) is a different value. Check the unit before assuming a calculator is wrong.

How to check the mode

Use the RAD/DEG control on the calculator workspace to switch between radians and degrees. Confirm that the selected unit matches the notation and instructions in your problem.

Related resources

Continue with the function graphing guide or learn to read scientific notation.