Add <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> to both sides of the equation.

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

Rewrite <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

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>θ</mi></mstyle></math> .

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

Simplify the right side.

Evaluate <math><mstyle displaystyle="true"><mi>arcsec</mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mstyle></math> .

The secant function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> to find the solution in the fourth quadrant.

Subtract <math><mstyle displaystyle="true"><mn>70.52877936</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> .

Find the period of <math><mstyle displaystyle="true"><mi>sec</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>360</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>360</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The period of the <math><mstyle displaystyle="true"><mi>sec</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> degrees in both directions.

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

Simplify the right side.

Evaluate <math><mstyle displaystyle="true"><mi>arcsec</mi><mrow><mo>(</mo><mo>-</mo><mn>3</mn><mo>)</mo></mrow></mstyle></math> .

The secant function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> to find the solution in the third quadrant.

Subtract <math><mstyle displaystyle="true"><mn>109.47122063</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> .

Find the period of <math><mstyle displaystyle="true"><mi>sec</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>360</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>360</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The period of the <math><mstyle displaystyle="true"><mi>sec</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> degrees in both directions.

List all of the solutions.

Consolidate <math><mstyle displaystyle="true"><mn>70.52877936</mn><mo>+</mo><mn>360</mn><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>250.52877936</mn><mo>+</mo><mn>360</mn><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mn>70.52877936</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> .

Consolidate <math><mstyle displaystyle="true"><mn>289.47122063</mn><mo>+</mo><mn>360</mn><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>109.47122063</mn><mo>+</mo><mn>360</mn><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mn>109.47122063</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> .

Do you know how to Solve for θ in Degrees sec(theta)^2-9=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 | one billion five hundred seventy-two million two hundred seventy-two thousand one hundred sixteen |
---|

- 1572272116 has 32 divisors, whose sum is
**3779393760** - The reverse of 1572272116 is
**6112722751** - Previous prime number is
**67**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 34
- Digital Root 7

Name | one billion six hundred forty million nine hundred forty-seven thousand three hundred eighty-one |
---|

- 1640947381 has 4 divisors, whose sum is
**1679108992** - The reverse of 1640947381 is
**1837490461** - Previous prime number is
**43**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 43
- Digital Root 7

Name | one billion five hundred ninety million three hundred seventy-one thousand two hundred sixteen |
---|

- 1590371216 has 256 divisors, whose sum is
**9820901376** - The reverse of 1590371216 is
**6121730951** - Previous prime number is
**127**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 35
- Digital Root 8