Draw a triangle in the plane with vertices <math><mstyle displaystyle="true"><mrow><mo>(</mo><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt><mo>,</mo><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> , <math><mstyle displaystyle="true"><mrow><mo>(</mo><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> , and the origin. Then <math><mstyle displaystyle="true"><mi>arcsin</mi><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is the angle between the positive x-axis and the ray beginning at the origin and passing through <math><mstyle displaystyle="true"><mrow><mo>(</mo><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt><mo>,</mo><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> . Therefore, <math><mstyle displaystyle="true"><mi>sec</mi><mrow><mo>(</mo><mi>arcsin</mi><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mrow></mfrac></mstyle></math> .

One to any power is one.

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mi>a</mi><mi>b</mi><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mi>n</mi></mrow></msup></mstyle></math> to distribute the exponent.

Apply the product rule to <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by adding the exponents.

Move <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

One to any power is one.

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

To write <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn></mrow></mfrac></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> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> , by multiplying each by an appropriate factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine.

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><msqrt><mn>4</mn></msqrt></mrow></mfrac></mstyle></math> .

Simplify the denominator.

Rewrite <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

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

Multiply the numerator by the reciprocal of the denominator.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><msqrt><mn>3</mn></msqrt></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><msqrt><mn>3</mn></msqrt></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><msqrt><mn>3</mn></msqrt></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><msqrt><mn>3</mn></msqrt></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><msqrt><mn>3</mn></msqrt></mrow></mfrac></mstyle></math> .

Raise <math><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

Rewrite <math><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>3</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Evaluate the exponent.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Do you know how to Find the Exact Value sec(arcsin(-1/2))? 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 | nine hundred one million three hundred forty-one thousand eight hundred nineteen |
---|

- 901341819 has 32 divisors, whose sum is
**1092960000** - The reverse of 901341819 is
**918143109** - Previous prime number is
**17**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 36
- Digital Root 9

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

- 1696971347 has 4 divisors, whose sum is
**1697097480** - The reverse of 1696971347 is
**7431796961** - Previous prime number is
**15313**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 53
- Digital Root 8

Name | four hundred nineteen million seven hundred thirty-seven thousand one hundred forty-two |
---|

- 419737142 has 32 divisors, whose sum is
**758346624** - The reverse of 419737142 is
**241737914** - Previous prime number is
**83**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 38
- Digital Root 2