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

The exact value of <math><mstyle displaystyle="true"><mi>arcsec</mi><mrow><mo>(</mo><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac></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>2</mn><mi>π</mi></mstyle></math> to find the solution in the third quadrant.

To write <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Combine fractions.

Combine <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>3</mn><mi>π</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>8</mn><mi>π</mi></mstyle></math> .

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>π</mi></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>2</mn><mi>π</mi></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>x</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> radians in both directions.

Do you know how to Solve for x in Radians sec(x)=- square root of 2? 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 | six hundred ninety-three million three hundred thirty-six thousand two hundred thirty-eight |
---|

- 693336238 has 16 divisors, whose sum is
**1195697664** - The reverse of 693336238 is
**832633396** - Previous prime number is
**167**

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

Name | sixty-five million eighty-five thousand forty-six |
---|

- 65085046 has 16 divisors, whose sum is
**105316848** - The reverse of 65085046 is
**64058056** - Previous prime number is
**701**

- Is Prime? no
- Number parity even
- Number length 8
- Sum of Digits 34
- Digital Root 7

Name | two hundred thirteen million seven hundred ninety-four thousand six hundred sixty-eight |
---|

- 213794668 has 8 divisors, whose sum is
**481038012** - The reverse of 213794668 is
**866497312** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 46
- Digital Root 1