The equations that involve the trigonometric functions of a variable are called trigonometric equations. In the upcoming discussion, we will try to find the solutions to such equations. These equations have one or more trigonometric ratios of unknown angles. For example, cos x -sin2 x = 0, is a trigonometric equation that does not satisfy all the values of x. Hence for such equations, we have to find the values of x or find the solution.

Trigonometric equations are, as the name implies, equations that involve trigonometric functions. Similar in many ways to solving polynomial equations or rational equations, only specific values of the variable will be solutions, if there are solutions at all. Often we will solve a trigonometric equation over a specified interval. However, just as often, we will be asked to find all possible solutions, and as trigonometric functions are periodic, solutions are repeated within each period. In other words, trigonometric equations may have an infinite number of solutions. Additionally, like rational equations, the domain of the function must be considered before we assume that any solution is valid. The period of both the sine function and the cosine function is 2π.
In other words, every 2π
units, the y-values repeat. If we need to find all possible solutions, then we must add 2πk,
where k
is an integer, to the initial solution. Recall the rule that gives the format for stating all possible solutions for a function where the period is 2π: