Unit Circle

To define the sine and cosine functions, we consider a point P(x, y) on the unit circle x² + y² = 1. Let θ be the angle measured counterclockwise in radians from the point (1, 0) to the point P(x, y) as shown in Figure 2.5.2. Both coordinates x and y depend on θ. The value of x is called the cosine of θ, and the value of y is the sine of θ. In symbols,

x = cos θ, y = sin θ.

The tangent of θ is defined by

tan θ = sin θ/cos θ.

Negative angles and angles greater than 2π radians are also allowed.