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 three hundred thirty-eight million three hundred thousand eight hundred fourteen

Interesting facts

  • 338300814 has 16 divisors, whose sum is 712212480
  • The reverse of 338300814 is 418003833
  • Previous prime number is 19

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 30
  • Digital Root 3

Name

Name four hundred thirty-seven million eight hundred eighty-three thousand four hundred five

Interesting facts

  • 437883405 has 8 divisors, whose sum is 467660416
  • The reverse of 437883405 is 504388734
  • Previous prime number is 817

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 42
  • Digital Root 6

Name

Name four hundred twenty-five million five hundred sixty thousand five hundred thirty-nine

Interesting facts

  • 425560539 has 8 divisors, whose sum is 571222800
  • The reverse of 425560539 is 935065524
  • Previous prime number is 149

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 39
  • Digital Root 3