Trigonometry Basics

Trigonometric Equations | Definition, Examples & How to Solve

Trigonometric equations are mathematical expressions that involve trigonometric functions (such as sine, cosine, tangent, etc.) and are set equal to a value. The goal is to find the values of the variable (usually an angle) that satisfy the equation.

For example, a simple trigonometric equation might be:

sin⁡(x) = 0.5

Solving this equation involves finding the values of x that make the sine of x equal to 0.5. The solutions could be periodic due to the nature of trigonometric functions.

Note: To solve the trigonometric equations, we will use the information that the period of sin x and cos x is 2π and the period of tan x is π.

Trigonometric Equations Examples

As Trigonometric Equations represent the relationships between different trigonometric functions, there can be infinitely many Trigonometric Equations. Some examples of Trigonometric Equations are:

• sin(x) = 1/√2
• cos(3x) = -1/2
• 2sin(2x) – 1 = 0
• tan(2x) + 3 = 0
• 2 cos(x) + sin(2x) = 1
• 3 sin(x) – 2 cos(2x) = 1
• 2 sin(3x) +  tan(x) = 0
• cot(x) + 2 cos(x) = 0
• 4 cos(2x) – 3 sin(3x) = 2