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:

1Trigonometric Equation

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution


2Trigonometric Equation

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution


3Trigonometric Equation

Sum to Product:

Trigonometric Operations

Divide by 2 and equate each factor to 0.

Trigonometric Operations

Trigonometric Solution


4Trigonometric Equation

Trigonometric Operations

Trigonometric Solution


5Trigonometric Equation

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution


6Trigonometric Equation

Trigonometric Operations

Trigonometric Solution


7Trigonometric Equation

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution


8Trigonometric Equation

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution


9Trigonometric Equation

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Operations

Trigonometric Solution