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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 tangent term.
If we restriction the domain of the tangent function to
we can use the inverse tangent function to
solve for reference angle
and then x.
The solution is
The period of the tangent function is and the period of this function is This means that the values will repeat every radians in both directions. Therefore, the exact solutions are n is an integer.
The approximate 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 equation.
Check answer x=4.1202023
Since the left side equals the right side when you substitute 4.1202023for x, then 4.1202023 is a solution.
Since the left side equals the right side when you substitute 13.54498 for x, then 13.54498 is a solution.
Graph the equation Note that the graph crosses the x-axis many times indicating many solutions.
The graph crosses the x-axis at 4.1202023. Since the period is , it crosses again at 4.1202023+9.424778=13.54498 and at 4.1202023+2(9.424778)=22.969758, etc.
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