If you would like an review of trigonometry, click on trigonometry.
Solve for x in the following equation.
There are an infinite number of solutions to this problem. To solve for x, you must first isolate the cosine function
If we restrict the domain of the cosine function to
we can use the
function to solve for x.
The cosine is positive in the first quadrant and the fourth quadrant. This
means that one solution is an angle that terminates in the first quadrant
and one solution is an angle that terminates in the fourth quadrant. The
second solution is
The period of cos function is This means that the values will repeat every radians. Therefore, the exact solutions are and where n is an integer. The approximate solutions are and
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.
Check answer x=0.541099525957
Check answer . x=5.74208578
Graph the equation
Note that the graph crosses the x-axis many times indicating many solutions. Two of the x-intercepts are located at 0.541099525957 and 5.74208578. This means that these are two solutions. Notice also that there is an x-intercept at 6.8244284833 which is equal to There is also an x-intercept at 12.02527108 which is equal to
If you would like to test yourself by working some problems similar to this example, click on Problem.
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