Let <math><mstyle displaystyle="true"><mi>u</mi><mo>=</mo><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> . Substitute <math><mstyle displaystyle="true"><mi>u</mi></mstyle></math> for all occurrences of <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>6</mn><mi>u</mi><mo>+</mo><mn>8</mn></mstyle></math> using the AC method.

Consider the form <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></mstyle></math> . Find a pair of integers whose product is <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> . In this case, whose product is <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Write the factored form using these integers.

Replace all occurrences of <math><mstyle displaystyle="true"><mi>u</mi></mstyle></math> with <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

If any individual factor on the left side of the equation is equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , the entire expression will be equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>+</mo><mn>2</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>+</mo><mn>2</mn><mo>=</mo><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> from both sides of the equation.

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

Simplify the right side.

Evaluate <math><mstyle displaystyle="true"><mi>arctan</mi><mrow><mo>(</mo><mo>-</mo><mn>2</mn><mo>)</mo></mrow></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"><mn>180</mn></mstyle></math> to find the solution in the third quadrant.

Simplify the expression to find the second solution.

Add <math><mstyle displaystyle="true"><mn>360</mn><mi>°</mi></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo><mn>63.43494882</mn><mo>-</mo><mn>180</mn><mi>°</mi></mstyle></math> .

The resulting angle of <math><mstyle displaystyle="true"><mn>116.56505117</mn><mi>°</mi></mstyle></math> is positive and coterminal with <math><mstyle displaystyle="true"><mo>-</mo><mn>63.43494882</mn><mo>-</mo><mn>180</mn></mstyle></math> .

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

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mn>180</mn></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"><mn>180</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> to every negative angle to get positive angles.

Add <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo><mn>63.43494882</mn></mstyle></math> to find the positive angle.

Subtract <math><mstyle displaystyle="true"><mn>63.43494882</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> .

List the new angles.

The period of the <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> degrees in both directions.

Set <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>+</mo><mn>4</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>+</mo><mn>4</mn><mo>=</mo><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> from both sides of the equation.

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

Simplify the right side.

Evaluate <math><mstyle displaystyle="true"><mi>arctan</mi><mrow><mo>(</mo><mo>-</mo><mn>4</mn><mo>)</mo></mrow></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"><mn>180</mn></mstyle></math> to find the solution in the third quadrant.

Simplify the expression to find the second solution.

Add <math><mstyle displaystyle="true"><mn>360</mn><mi>°</mi></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo><mn>75.96375653</mn><mo>-</mo><mn>180</mn><mi>°</mi></mstyle></math> .

The resulting angle of <math><mstyle displaystyle="true"><mn>104.03624346</mn><mi>°</mi></mstyle></math> is positive and coterminal with <math><mstyle displaystyle="true"><mo>-</mo><mn>75.96375653</mn><mo>-</mo><mn>180</mn></mstyle></math> .

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

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mn>180</mn></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"><mn>180</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> to every negative angle to get positive angles.

Add <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo><mn>75.96375653</mn></mstyle></math> to find the positive angle.

Subtract <math><mstyle displaystyle="true"><mn>75.96375653</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> .

List the new angles.

The period of the <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> degrees in both directions.

The final solution is all the values that make <math><mstyle displaystyle="true"><mrow><mo>(</mo><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>+</mo><mn>4</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> true.

Consolidate <math><mstyle displaystyle="true"><mn>104.03624346</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>104.03624346</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mn>104.03624346</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> .

Do you know how to Solve for θ in Degrees tan(theta)^2+6tan(theta)+8=0? 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 | nine hundred forty-eight million seven hundred twenty-three thousand nine hundred |
---|

- 948723900 has 64 divisors, whose sum is
**4098488544** - The reverse of 948723900 is
**009327849** - Previous prime number is
**5**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 42
- Digital Root 6

Name | one billion six hundred forty million four hundred sixty-three thousand seventy-eight |
---|

- 1640463078 has 32 divisors, whose sum is
**3487161600** - The reverse of 1640463078 is
**8703640461** - Previous prime number is
**103**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 39
- Digital Root 3

Name | two hundred twenty-three million two hundred fifty thousand four hundred sixty-nine |
---|

- 223250469 has 8 divisors, whose sum is
**298102080** - The reverse of 223250469 is
**964052322** - Previous prime number is
**689**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 33
- Digital Root 6