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SOLVING TRIGONOMETRIC EQUATIONS

**Note: **If you would like a review of trigonometry, click on
trigonometry.

Example 1: **Solve for x in the following equation.**

There are an infinite number of solutions to this problem. To solve for x,
set the equation equal to zero and factor.

then

when
when
,
and when

when
and
This is
impossible because

The exact value solutions are
and
The approximate value of these solutions are

and

where n is an integer.

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:

Check the answer
*x*=1.5707963

Left Side:

Right Side:

Since the left side equals the right side when you substitute 1.5707963for x, then 1.5707963 is a solution.

Check the answer
*x*=4.71238898

Left Side:

Right Side:

Since the left side equals the right side when you substitute
4.71238898for x, then
4.71238898 is a solution.

Graphical Check:

Graph the equation
Note that the graph
crosses the x-axis many times indicating many solutions.

Note that it crosses at 1.5707963. Since the period is
,
it crosses again at
1.5707963+6.2831853=7.85398 and at
<*tex*2*html*_{c}*omment*_{m}*ark*>
1.5707963+2(6.2831853)=14.137167, etc.

Note that it crosses at
4.71238898. Since the period is
,
it crosses again at
4.71238898+6.2831853=10.99557 and at
<*tex*2*html*_{c}*omment*_{m}*ark*>
4.71238898+2(6.2831853)=17.27876, etc.

**
If you would like to work another example, click on Example.
**

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.**

If you would like to go back to the previous section, click on *
***previous**.

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[Algebra]
[Trigonometry]
[Geometry]
[Differential Equations]
[Calculus]
[Complex Variables]
[Matrix Algebra]
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Author:
Nancy Marcus

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