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 one billion seven hundred sixty-eight million one hundred seventy-eight thousand seven hundred fifty-one

Interesting facts

  • 1768178751 has 32 divisors, whose sum is 2528547840
  • The reverse of 1768178751 is 1578718671
  • Previous prime number is 1741

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 51
  • Digital Root 6

Name

Name forty-four million fifty-seven thousand two hundred thirty-five

Interesting facts

  • 44057235 has 16 divisors, whose sum is 72923040
  • The reverse of 44057235 is 53275044
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 8
  • Sum of Digits 30
  • Digital Root 3

Name

Name one billion two hundred eighty million seven hundred sixty-seven thousand nine hundred ninety-six

Interesting facts

  • 1280767996 has 8 divisors, whose sum is 2881728000
  • The reverse of 1280767996 is 6997670821
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 55
  • Digital Root 1