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

Subtract <math><mstyle displaystyle="true"><mn>5</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> from <math><mstyle displaystyle="true"><mn>8</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> to both sides of the equation.

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>9</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> .

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>3</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> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</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.

The exact value of <math><mstyle displaystyle="true"><mi>arctan</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>45</mn></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>45</mn></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.

Consolidate the answers.

Do you know how to Solve for θ in Degrees 8tan(theta)-12=5tan(theta)-9? 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 fifty-one million one hundred forty-five thousand three hundred seven |
---|

- 1051145307 has 4 divisors, whose sum is
**1167939240** - The reverse of 1051145307 is
**7035411501** - Previous prime number is
**9**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 27
- Digital Root 9

Name | one hundred eighty-eight million two hundred twelve thousand five hundred fifty |
---|

- 188212550 has 16 divisors, whose sum is
**300776112** - The reverse of 188212550 is
**055212881** - Previous prime number is
**41**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 32
- Digital Root 5

Name | six hundred sixty-eight million thirty-nine thousand five hundred forty-six |
---|

- 668039546 has 8 divisors, whose sum is
**1002287520** - The reverse of 668039546 is
**645930866** - Previous prime number is
**4679**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 47
- Digital Root 2