Trigonometry Examples

Solve for ? 3tan(x)^2=0
Step 1
Divide each term in by and simplify.
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Step 1.1
Divide each term in by .
Step 1.2
Simplify the left side.
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Step 1.2.1
Cancel the common factor of .
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Step 1.2.1.1
Cancel the common factor.
Step 1.2.1.2
Divide by .
Step 1.3
Simplify the right side.
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Step 1.3.1
Divide by .
Step 2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3
Simplify .
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Step 3.1
Rewrite as .
Step 3.2
Pull terms out from under the radical, assuming positive real numbers.
Step 3.3
Plus or minus is .
Step 4
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Step 5
Simplify the right side.
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Step 5.1
The exact value of is .
Step 6
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 7
Add and .
Step 8
Find the period of .
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Step 8.1
The period of the function can be calculated using .
Step 8.2
Replace with in the formula for period.
Step 8.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 8.4
Divide by .
Step 9
The period of the function is so values will repeat every radians in both directions.
, for any integer
Step 10
Consolidate the answers.
, for any integer