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.
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One to any power is one.
Use the power rule to distribute the exponent.
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Apply the product rule to .
Apply the product rule to .
Multiply by by adding the exponents.
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Move .
Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
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 .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Rewrite as .
Simplify the denominator.
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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.
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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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