Trigonometry Examples

Solve for x 2=tan(x)(5)
Step 1
Rewrite the equation as .
Step 2
Divide each term in by and simplify.
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Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Cancel the common factor of .
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Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Divide by .
Step 3
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Step 4
Simplify the right side.
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Step 4.1
Evaluate .
Step 5
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.
Step 6
Solve for .
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Step 6.1
Remove parentheses.
Step 6.2
Remove parentheses.
Step 6.3
Add and .
Step 7
Find the period of .
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Step 7.1
The period of the function can be calculated using .
Step 7.2
Replace with in the formula for period.
Step 7.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 7.4
Divide by .
Step 8
The period of the function is so values will repeat every radians in both directions.
, for any integer
Step 9
Consolidate and to .
, for any integer