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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 sine term.
The period of the sin function is This means that the values will repeat every radians in both directions. Therefore, the exact solutions are and where n is an integer.
The approximate 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.
Check the answer x=0.131705318835
Since the left side equals the right side when you substitute 0.131705318835 for x, then 0.131705318835 is a solution.
Check the answer x=1.29629134189
Since the left side equals the right side when you substitute 1.29629134189for x, then 1.29629134189 is a solution.
Graph the equation
Note that the graph crosses the x-axis many times indicating many solutions. Note that it crosses at 0.131705318835. Since the period is , it crosses again at 0.131705318835 + 2.85599 = 2.98769864028 and at 0.131705318835 + 2( 2.85599 ) = 5.843685, etc.
The graph crosses at 1.29629134189. Since the period is , it will cross again at and at , etc.
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