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.
when when , and when
when and This is impossible because
The exact value solutions are
The approximate value of these 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
Check the answer x=1.5707963
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
Since the left side equals the right side when you substitute 4.71238898for x, then 4.71238898 is a solution.
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 <tex2htmlcommentmark> 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 <tex2htmlcommentmark> 4.71238898+2(6.2831853)=17.27876, etc.
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.
If you would like to go back to the equation table of contents, click on Contents.
S.O.S MATHematics home page