Trigonometric Equations

Trigonometric equations involve trigonometric functions that are periodic and therefore their solutions can occur in one or two quadrants and all revolutions.

To solve a trigonometric equation make the changes needed to work with only one trigonometric function, then if needed, use fundamental trigonometric identities.


Examples

Solve the trigonometric equation:

1.Trigonometric Equation

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution


2.Trigonometric Equation

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution


3.Trigonometric Equation

Sum to Product:

Trigonometric Operations

Divide by 2 and equate each factor to 0.

Trigonometric Operations

Trigonometric Solution


4.Trigonometric Equation

Trigonometric Operations

Trigonometric Solution


5.Trigonometric Equation

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution


6.Trigonometric Equation

Trigonometric Operations

Trigonometric Solution


7.Trigonometric Equation

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution


8.Trigonometric Equation

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution


9.Trigonometric Equation

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution