Trigonometric Equations


A trigonometric equation is an equation which contains a trigonometric expression with a variable, such as sinx or tanx. Some trigonometric equations are identities, that is, they are true for all values of the variables for which the expressions are defined, some equations are true only for some values

Example 1

Solve the equation: sin x= 1/2 , 0≤x < 2π .


The restriction 0≤x < 2π means that the angle x is within the first revolution only and measured in the
counter-clockwise direction (positive direction).

Since the value of sinx is positive, then x lies in Quadrant I or II.

Now, sin π/6 = 1/2 and so π/6 serves as the reference angle.

In Quadrant I: x = π/6 (Use the reference angle itself.)

In Quadrant II: x = π - π/6 = 5π/6

The solutions are π/6 and 5 π/6.

Example 2

Example 3

Try these problems


Solve the trigonometric equations