Relationship of Sine and Cosine to the Unit Circle

degrees

Drag the blue radius around the circle.

You have moved θ = 0 radians

The

x

coordinate of

P

on the circle is given by cos(θ) = 1.

The

y

coordinate of

P

on the circle is given by sin(θ) = 0.

Rotate the blue arrow around the unit circle. The distance travelled from the point (1,0) to a point (

x

,

y

) on a unit circle corresponds to the angle in radians between the positive

x

axis and the line segment from the origin to the point (

x

,

y

). The

x

coordinate corresponds to the cosine of the angle and the

y

coordinate corresponds to the sine of the angle. You can also see the angle in degrees.