Sine and Cosine

The two definitions, with circles and right triangles, can be seen to be equivalent using similar triangles.

Table 2.5.1 gives the values of sin θ and cos θ for some important values of θ.

A useful identity which follows from the unit circle equation

x² + y² = 1

is

sin² θ + cos² θ = 1.

Here sin² θ means (sin θ)².

Figure 2.5.4 shows the graphs of sin θ and cos θ, which look like waves that oscillate between 1 and -1 and repeat every 2π radians.