Course: Trigonometry
Topic: Right Triangle Trigonometry
Subtopic: soh-cah-toa Definition


We previously defined the six trig functions in terms of x, y, and r. In this lesson we redefine them using slightly different terminology. "soh-cah-toa" is an easy way to remember the ratios that define the three main trig functions. Think of "o" as the side opposite the angle, "a" as the side adjacent to the angle, and h as the hypotentuse. Then soh-cah-toa means sine = opposite over hypotenuse, cosine = adjacent over hypotenuse, and tangent = opposite over adjacent.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: cofunction

Memorize the soh-cah-toa definitions of the first three trig functions:

Six trig functions defined as soh cah toa. For example, sine of theta is opposite over hypotenuse. S for sine, O for opposite, H for hypotenuse.

Memorize the "special" values mentioned in objective 2.1.3 above:

Chart with exact values of sine, cosine, and tangent of 30, 45, and 60 degrees.

Know how to use the cofunction theorem:

Cofunction theorem says trig function of an angle is equal to its cofunction of the complementary angle and visa versa.

Mini-Lectures and Examples

STUDY: SOH-CAH-TOA Definition of Trig Functions & Calculators & Reference Angles

Supplemental Resources (optional)

Videos from James Sousa's MathIsPower4U:

Introduction to Trigonometric Functions Using Triangles
30-60-90 and 45-45-90 Reference Triangles
Solving 30-60-90 and 45-45-90 Right Triangles

Solve a 30-60-90 Triangle
Solve a 45-45-90 Right Triangle

rev. 2020-10-10