Precalculus Examples

Solve for x tan(x)=5
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Evaluate .
The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from to find the solution in the fourth quadrant.
Simplify the expression to find the second solution.
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Remove the parentheses around the expression .
Add and .
Find the period.
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The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
Consolidate the answers.
, for any integer
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