Solve for x in Radians tan(x)^2=1/3

Solve for x in Radians tan(x)^2=1/3
Take the square root of both sides of the equation to eliminate the exponent on the left side.
Simplify .
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Rewrite as .
Any root of is .
Multiply by .
Combine and simplify the denominator.
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
The complete solution is the result of both the positive and negative portions of the solution.
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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 .
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Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
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The exact value of is .
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 .
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To write as a fraction with a common denominator, multiply by .
Combine fractions.
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Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Move to the left of .
Add and .
Find the period of .
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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 .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
Solve for in .
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Take the inverse tangent of both sides of the equation to extract from inside the tangent.
Simplify the right side.
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The exact value of is .
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.
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Add to .
The resulting angle of is positive and coterminal with .
Find the period of .
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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 .
Divide by .
Add to every negative angle to get positive angles.
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Add to to find the positive angle.
To write as a fraction with a common denominator, multiply by .
Combine fractions.
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Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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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.
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Consolidate and to .
, for any integer
Consolidate and to .
, for any integer
, for any integer
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Name

Name four hundred sixty-six million five hundred fourteen thousand two hundred seventy-four

Interesting facts

  • 466514274 has 8 divisors, whose sum is 933028560
  • The reverse of 466514274 is 472415664
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 39
  • Digital Root 3

Name

Name six hundred eighty-eight million three hundred thirty-four thousand eight hundred eighty-five

Interesting facts

  • 688334885 has 16 divisors, whose sum is 728593344
  • The reverse of 688334885 is 588433886
  • Previous prime number is 67

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 53
  • Digital Root 8

Name

Name eighty-five million nine hundred fifteen thousand three

Interesting facts

  • 85915003 has 4 divisors, whose sum is 86274720
  • The reverse of 85915003 is 30051958
  • Previous prime number is 239

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 8
  • Sum of Digits 31
  • Digital Root 4