Angle Rotation Simulator

Rotate an angle and see radians, quadrant, reference angle, and coterminal angles

Angle (degrees)

Angle Rotation Rules

radians = degrees x pi / 180

coterminal angles = theta + 360k degrees

reference angle = acute angle to the x-axis

positive angles rotate counterclockwise

Angle rotation is the foundation for unit circle trigonometry. It explains quadrants, trig signs, reference angles, and why many angles share the same terminal side.

Teaching Example: 135 degrees is in quadrant II, has reference angle 45 degrees, and is coterminal with -225 degrees and 495 degrees.

Frequently Asked Questions

What is a terminal side?▼

The terminal side is the ray position after rotating from the positive x-axis by the given angle.

What are coterminal angles?▼

Coterminal angles end at the same terminal side and differ by multiples of 360 degrees or 2pi radians.

What is a reference angle?▼

A reference angle is the acute angle between the terminal side and the x-axis.

How are degrees converted to radians?▼

Multiply degrees by pi/180 to convert to radians.

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