TrigoSystems

Modules · Module 04

Trigonometric ratios

In a right triangle, each acute angle has three primary ratios. They convert an angle into a comparison of sides, and a comparison of sides into an angle.

sin θ = opp / hyp cos θ = adj / hyp tan θ = opp / adj

Primary ratios

Sine of an acute angle is opposite over hypotenuse.

Cosine of an acute angle is adjacent over hypotenuse.

Tangent of an acute angle is opposite over adjacent.

Reciprocals

csc θ = 1 / sin θ, sec θ = 1 / cos θ, cot θ = 1 / tan θ.

These are useful when a side you need is in the denominator of a primary ratio.

Cofunctions

sin θ = cos(90° − θ), and tan θ = cot(90° − θ).

The two acute angles in a right triangle are complementary, so each ratio of one is the cofunction of the other.