Take the square root of both sides of the equation to eliminate the exponent on the left side.

Rewrite <math><mstyle displaystyle="true"><msqrt><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>1</mn></msqrt></mrow><mrow><msqrt><mn>3</mn></msqrt></mrow></mfrac></mstyle></math> .

Any root of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><mn>3</mn></msqrt></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><msqrt><mn>3</mn></msqrt></mrow></mfrac></mstyle></math> .

Combine and simplify the denominator.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><mn>3</mn></msqrt></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><msqrt><mn>3</mn></msqrt></mrow></mfrac></mstyle></math> .

Raise <math><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msup><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>3</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Evaluate the exponent.

First, use the positive value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the first solution.

Next, use the negative value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> 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 <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Take the inverse tangent of both sides of the equation to extract <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> from inside the tangent.

Simplify the right side.

The exact value of <math><mstyle displaystyle="true"><mi>arctan</mi><mrow><mo>(</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>3</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> .

The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> to find the solution in the fourth quadrant.

Simplify <math><mstyle displaystyle="true"><mi>π</mi><mo>+</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> .

To write <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>6</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> .

Combine fractions.

Combine <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>6</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Move <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>6</mn><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Find the period of <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mrow><mo>|</mo><mi>b</mi><mo>|</mo></mrow></mrow></mfrac></mstyle></math> .

Replace <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> in the formula for period.

The absolute value is the distance between a number and zero. The distance between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The period of the <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> radians in both directions.

Take the inverse tangent of both sides of the equation to extract <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> from inside the tangent.

Simplify the right side.

The exact value of <math><mstyle displaystyle="true"><mi>arctan</mi><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>3</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> .

The tangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> to find the solution in the third quadrant.

Simplify the expression to find the second solution.

Add <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>-</mo><mi>π</mi></mstyle></math> .

The resulting angle of <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> is positive and coterminal with <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>-</mo><mi>π</mi></mstyle></math> .

Find the period of <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mrow><mo>|</mo><mi>b</mi><mo>|</mo></mrow></mrow></mfrac></mstyle></math> .

Replace <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> in the formula for period.

The absolute value is the distance between a number and zero. The distance between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> to every negative angle to get positive angles.

Add <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> to find the positive angle.

To write <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>6</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> .

Combine fractions.

Combine <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>6</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Move <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>6</mn><mi>π</mi></mstyle></math> .

List the new angles.

The period of the <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> radians in both directions.

List all of the solutions.

Consolidate <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>+</mo><mi>π</mi><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>7</mn><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>+</mo><mi>π</mi><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>+</mo><mi>π</mi><mi>n</mi></mstyle></math> .

Consolidate <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>+</mo><mi>π</mi><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>+</mo><mi>π</mi><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>+</mo><mi>π</mi><mi>n</mi></mstyle></math> .

Do you know how to Solve for x in Radians tan(x)^2=1/3? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

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

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

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

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

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

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

Name | eighty-five million nine hundred fifteen thousand three |
---|

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

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