Convert to Trigonometric Form (1+cos(2y))/(sin(2y))

Convert to Trigonometric Form (1+cos(2y))/(sin(2y))
This is the trigonometric form of a complex number where is the modulus and is the angle created on the complex plane.
The modulus of a complex number is the distance from the origin on the complex plane.
where
Substitute the actual values of and .
Find .
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Raising to any positive power yields .
Apply the product rule to .
Multiply by .
Separate fractions.
Convert from to .
Simplify the expression.
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Divide by .
Rewrite as .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
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Simplify each term.
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Multiply by .
Multiply by .
Multiply by .
Multiply .
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Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Add and .
Apply the distributive property.
Simplify.
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Multiply by .
Rewrite in terms of sines and cosines.
Apply the product rule to .
One to any power is one.
Combine and .
Convert from to .
Add and .
Rewrite in a factored form.
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Rewrite the middle term.
Rearrange terms.
Factor first three terms by perfect square rule.
Rewrite as .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
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Simplify each term.
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Multiply .
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Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Multiply .
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Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Reorder the factors of .
Add and .
Add and .
Factor using the perfect square rule.
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Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Rewrite the polynomial.
Factor using the perfect square trinomial rule , where and .
Pull terms out from under the radical, assuming positive real numbers.
The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.
Substitute the values of and .
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Name

Name one billion seven hundred seventy-five million six thousand six hundred eighty-five

Interesting facts

  • 1775006685 has 16 divisors, whose sum is 2388394800
  • The reverse of 1775006685 is 5866005771
  • Previous prime number is 109

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 45
  • Digital Root 9

Name

Name six hundred thirty million forty-five thousand two hundred fifty

Interesting facts

  • 630045250 has 32 divisors, whose sum is 1211339376
  • The reverse of 630045250 is 052540036
  • Previous prime number is 25

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 25
  • Digital Root 7

Name

Name eight hundred nine million one hundred twenty-seven thousand seven hundred sixteen

Interesting facts

  • 809127716 has 32 divisors, whose sum is 1929733632
  • The reverse of 809127716 is 617721908
  • Previous prime number is 991

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 41
  • Digital Root 5