Simplify cos(arcsin(5/13))

Simplify cos(arcsin(5/13))
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 .
Divide by .
One to any power is one.
Apply the product rule to .
Raise to the power of .
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 numerator.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Simplify the denominator.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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Name

Name five hundred ninety-six million eight hundred ninety-nine thousand two hundred seven

Interesting facts

  • 596899207 has 4 divisors, whose sum is 613031656
  • The reverse of 596899207 is 702998695
  • Previous prime number is 37

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 55
  • Digital Root 1

Name

Name one billion nine hundred nine million nine hundred sixty-seven thousand six hundred thirty-four

Interesting facts

  • 1909967634 has 32 divisors, whose sum is 4246741440
  • The reverse of 1909967634 is 4367699091
  • Previous prime number is 17747

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 54
  • Digital Root 9

Name

Name seventy-six million nine hundred fifty-eight thousand five hundred sixty-nine

Interesting facts

  • 76958569 has 4 divisors, whose sum is 81009040
  • The reverse of 76958569 is 96585967
  • Previous prime number is 19

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 8
  • Sum of Digits 55
  • Digital Root 1