Circular sense of movements

Angle of rotation

(aka oriented angles) in standard position

= angle that has the vertex in origin: initial side (the positive ray of the x-axis), terminal side (the other side of the angle), sense of orientation (counterclockwise +, clockwise - )

Co-terminal angles

Reference angle

of a standard position angle

= the acute angle (between 0 and 90 degrees) determined by the terminal side with the positive/negative ray of the x-axis.

Click on the carousel image below to see angles in standard position and the corresponding reference angle.

Reference angle of a given angle x are used to find the sine and cosine of the angle x.

Play & Learn applets

(click on the buttons below)

1. Choose the positive co-terminal angles of 30 degrees

2. What is the value of the reference angle of 240 degrees?