## SOLVING TRIGONOMETRIC EQUATIONS

Note:

If you would like an review of trigonometry, click on trigonometry.

Solve for x in the following equation.

Example 4:

There are an infinite number of solutions to this problem. To solve for x, you must first isolate the tangent function.

Isolate the tangent term.

If we restrict the domain of the tangent function to , we can use the arctan function to solve for x.

The period of tan function is This means that the values will repeat every radians. Therefore, the exact solutions are The approximate solutions are

These solutions may or may not be the answers to the original problem. You much check them, either numerically or graphically, with the original equation.

Numerical Check:

• Left Side:

• Right Side:        0

Since the left side equals the right side when you substitute 0.750929062398 for x, then 0.750929062398 is a solution.

• Left Side:

• Right Side:        0

Since the left side equals the right side when you substitute 3.89252171599for x, then 3.89252171599 is a solution.

Graphical Check:

Graph the equation

Note that the graph crosses the x-axis many times indicating many solutions. One of the x-intercepts is located at 0.750929062398. This means that this is a solution. Notice that the distance between each x-intercepts is

If you would like to test yourself by working some problems similar to this example, click on Problem.

IF you would like to go to the next section, click on Next.

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[Algebra] [Trigonometry]
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Author: Nancy Marcus