Add <math><mstyle displaystyle="true"><mn>5</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> to both sides of the equation.

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>10</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><mn>5</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Reorder terms.

For a polynomial of the form <math><mstyle displaystyle="true"><mi>a</mi><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> , rewrite the middle term as a sum of two terms whose product is <math><mstyle displaystyle="true"><mi>a</mi><mo>⋅</mo><mi>c</mi><mo>=</mo><mn>6</mn><mo>⋅</mo><mn>1</mn><mo>=</mo><mn>6</mn></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mo>-</mo><mn>5</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> plus <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math>

Apply the distributive property.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

Factor out the greatest common factor (GCF) from each group.

Factor the polynomial by factoring out the greatest common factor, <math><mstyle displaystyle="true"><mn>3</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn></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"><mn>3</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mn>3</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn><mo>=</mo><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to both sides of the equation.

Divide each term in <math><mstyle displaystyle="true"><mn>3</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>=</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>3</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>=</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

The tangent function is positive in the first and third 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 fourth quadrant.

Add <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>18.43494882</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> .

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"><mn>2</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mn>2</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn><mo>=</mo><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to both sides of the equation.

Divide each term in <math><mstyle displaystyle="true"><mn>2</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>=</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>2</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>=</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Simplify the left side.

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

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

The tangent function is positive in the first and third 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 fourth quadrant.

Add <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>26.56505117</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> .

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><mn>3</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><mn>2</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> true.

Consolidate <math><mstyle displaystyle="true"><mn>18.43494882</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>198.43494882</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mn>18.43494882</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> .

Consolidate <math><mstyle displaystyle="true"><mn>26.56505117</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>206.56505117</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mn>26.56505117</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> .

Do you know how to Solve for θ in Degrees 6tan(theta)^2-10tan(theta)+1=-5tan(theta)? 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 | one billion nine hundred fifty-one million four hundred ninety thousand eight hundred seventy-two |
---|

- 1951490872 has 32 divisors, whose sum is
**6598470600** - The reverse of 1951490872 is
**2780941591** - Previous prime number is
**541**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 46
- Digital Root 1

Name | eight hundred sixty-two million seven hundred seventy-one thousand nine hundred seventy-four |
---|

- 862771974 has 32 divisors, whose sum is
**1786444800** - The reverse of 862771974 is
**479177268** - Previous prime number is
**349**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 51
- Digital Root 6

Name | four hundred sixty-five million three hundred ninety-one thousand one hundred seventy-seven |
---|

- 465391177 has 8 divisors, whose sum is
**485847936** - The reverse of 465391177 is
**771193564** - Previous prime number is
**5737**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 43
- Digital Root 7