Definitions of sine, cosine, tangent and cotangent

The ordinate of the point obtained by rotating P(1, 0) through α is called the sine of α (sin α), and its abscissa the cosine (cos α). The tangent is tan α = sin α : cos α (cos α ≠ 0, i.e. α ≠ π/2 + πk), and the cotangent is cot α = cos α : sin α (sin α ≠ 0, i.e. α ≠ πk). Since the coordinates of a point on the unit circle lie between −1 and 1, −1 ≤ sin α ≤ 1 and −1 ≤ cos α ≤ 1. Key values: sin 0 = 0, sin π/6 = 1/2, sin π/4 = √2/2, sin π/3 = √3/2, sin π/2 = 1; cos goes in the reverse order: 1, √3/2, √2/2, 1/2, 0. tan π/6 = √3/3, tan π/4 = 1, tan π/3 = √3. The simplest equations: sin t = 0 gives t = πk; cos t = 0 gives t = π/2 + πk; sin t = 1 gives t = π/2 + 2πk; cos t = 1 gives t = 2πk (k ∈ Z).