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

Overview

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.

Objectives

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

• 2.1.1 Use the soh-cah-toa definition to find the six trig functions of a given angle
• 2.1.2 Evaluate the six trig functions at common angles
• 2.1.3 Know by memory the sine, cosine, and tangent of 30°, 45°, and 60°
• 2.1.4 Evaluate the three cofunctions using the cofunction theorem

Terminology

Define: cofunction

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

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

Know how to use the cofunction theorem:

Supplemental Resources (optional)

Videos from James Sousa's MathIsPower4U:
Mini-Lessons:
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
Examples:
Solve a 30-60-90 Triangle
Solve a 45-45-90 Right Triangle