# Solve for x in Radians tan(3x)^2=3

Solve for x in Radians tan(3x)^2=3
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Set up each of the solutions to solve for .
Solve for in .
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
The exact value of is .
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Multiply and .
Multiply by .
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.
Solve for .
Simplify.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Reorder and .
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Multiply and .
Multiply by .
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
Solve for in .
Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
The exact value of is .
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Multiply and .
Multiply by .
The tangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Simplify the expression to find the second solution.
The resulting angle of is positive and coterminal with .
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Multiply and .
Multiply by .
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Add to every negative angle to get positive angles.
Add to to find the positive angle.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Move to the left of .
Subtract from .
List the new angles.
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
List all of the solutions.
, for any integer
Consolidate the solutions.
Consolidate and to .
, for any integer
Consolidate and to .
, for any integer
, for any integer
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