# Find the Exact Value sec(arcsin(-1/2))

Find the Exact Value sec(arcsin(-1/2))
Draw a triangle in the plane with vertices , , and the origin. Then is the angle between the positive x-axis and the ray beginning at the origin and passing through . Therefore, is .
Simplify the denominator.
One to any power is one.
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
One to any power is one.
Raise to the power of .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Rewrite as .
Simplify the denominator.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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### Name

Name nine hundred one million three hundred forty-one thousand eight hundred nineteen

### Interesting facts

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

### Basic properties

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

### Name

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

### Interesting facts

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

### Basic properties

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

### Name

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

### Interesting facts

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

### Basic properties

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