Note:
If you would like an review of trigonometry, click on trigonometry.
Solve for x in the following equation.
Example 2:
There are an infinite number of solutions to this problem. To solve for x, isolate the sine term.
The sine function is positive in the first and second quadrant. If the reference angle is , the angle that terminates in the second quadrant is
The period of sin function is This means that the values will repeat every radians. Therefore, the 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 answer . x=0.304692654015
Check answer . x=2.83689999957
Graphical Check:
Graph the equation
Note that the graph crosses the x-axis many times indicating many solutions.
Note that it crosses at (one of the solutions). Since the period of the function is , the graph crosses again at 2.83689999957+6.28318530718=9.12 and again at , etc. The graph also crosses at 0.304692654015 (another solution we found). Since the period is , it will cross again at and at , 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 equation table of contents, click on Contents.
This site was built to accommodate the needs of students. The topics and problems are what students ask for. We ask students to help in the editing so that future viewers will access a cleaner site. If you feel that some of the material in this section is ambiguous or needs more clarification, please let us know by e-mail.