Solving Trigonometric Equations The following equation is called an identity: This equation is true for all real numbers x.

Solving Trigonometric Equations The following equation is called a conditional equation: This equation is true only when x = 5, or we could say on the condition that x = 5. The focus of this presentation will be on conditional trigonometric equations.

 Example 1: Solve: Think about where cosine will have this value on the unit circle: Recall that cosine is the first coordinate of the points on the unit circle.

The two rays through these two points are defined by … The values of x that solve the equation are …

Visualize each of these rays rotating counter clockwise 2 π units (one complete revolution). The terminal rays would pass through the same points. Continuing to rotate multiples of 2 π units would yield the same results.

This means there are infinitely many solutions to the equation by adding multiples of 2 π units.

 Example 2: Solve: Solve the equation for sin x.

Think about where sine will have this value on the unit circle: Recall that sine is the second coordinate of the points on the unit circle.

The two rays through these two points are defined by … The values of x that solve the equation are …

Visualize each of these rays rotating counter clockwise 2 π units (one complete revolution). The terminal rays would pass through the same points. Continuing to rotate multiples of 2 π units would yield the same results.

This means there are infinitely many solutions to the equation by adding multiples of 2 π units.