Subtract <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> .

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>8</mn><mo>⋅</mo><mn>3</mn><mo>=</mo><mn>24</mn></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mn>10</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>10</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> as <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> plus <math><mstyle displaystyle="true"><mn>6</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>2</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>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> .

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from 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><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><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> .

Simplify the right side.

Move the negative in front of the fraction.

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><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><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>26.56505117</mn><mo>-</mo><mn>180</mn><mi>°</mi></mstyle></math> .

The resulting angle of <math><mstyle displaystyle="true"><mn>153.43494882</mn><mi>°</mi></mstyle></math> is positive and coterminal with <math><mstyle displaystyle="true"><mo>-</mo><mn>26.56505117</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>26.56505117</mn></mstyle></math> to find the positive angle.

Subtract <math><mstyle displaystyle="true"><mn>26.56505117</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"><mn>4</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>+</mo><mn>3</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mn>4</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>+</mo><mn>3</mn><mo>=</mo><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from both sides of the equation.

Divide each term in <math><mstyle displaystyle="true"><mn>4</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>=</mo><mo>-</mo><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>4</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>=</mo><mo>-</mo><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>4</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> .

Simplify the right side.

Move the negative in front of the fraction.

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><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><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>36.86989764</mn><mo>-</mo><mn>180</mn><mi>°</mi></mstyle></math> .

The resulting angle of <math><mstyle displaystyle="true"><mn>143.13010235</mn><mi>°</mi></mstyle></math> is positive and coterminal with <math><mstyle displaystyle="true"><mo>-</mo><mn>36.86989764</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>36.86989764</mn></mstyle></math> to find the positive angle.

Subtract <math><mstyle displaystyle="true"><mn>36.86989764</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><mn>2</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>4</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>+</mo><mn>3</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> true.

Do you know how to Solve for θ in Degrees 8tan(theta)^2+10tan(theta)+10=7? 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 seventy-two million four hundred nine thousand seven hundred twenty |
---|

- 1072409720 has 64 divisors, whose sum is
**4347219456** - The reverse of 1072409720 is
**0279042701** - Previous prime number is
**1151**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 32
- Digital Root 5

Name | one billion nine hundred six million four hundred fifty-five thousand four hundred sixty-eight |
---|

- 1906455468 has 16 divisors, whose sum is
**5719366440** - The reverse of 1906455468 is
**8645546091** - Previous prime number is
**3**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 48
- Digital Root 3

Name | one billion eight hundred seventy-nine million five hundred thirty-one thousand five hundred twenty |
---|

- 1879531520 has 32768 divisors, whose sum is
**438961762944** - The reverse of 1879531520 is
**0251359781** - Previous prime number is
**5**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 41
- Digital Root 5