Find Amplitude, Period, and Phase Shift y=cos(4pix-5/3)

Find Amplitude, Period, and Phase Shift y=cos(4pix-5/3)
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Find the amplitude .
Amplitude:
Find the period of .
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The period of the function can be calculated using .
Replace with in the formula for period.
is approximately which is positive so remove the absolute value
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Find the phase shift using the formula .
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The phase shift of the function can be calculated from .
Phase Shift:
Replace the values of and in the equation for phase shift.
Phase Shift:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Multiply .
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Multiply and .
Phase Shift:
Multiply by .
Phase Shift:
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the right)
Vertical Shift: None
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Name

Name two billion one hundred twenty-five million seven hundred seventy-one thousand seven hundred seventy-six

Interesting facts

  • 2125771776 has 8192 divisors, whose sum is 141264103680
  • The reverse of 2125771776 is 6771775212
  • Previous prime number is 9

Basic properties

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

Name

Name one billion one hundred thirty-four million three hundred eight thousand seven hundred seventy-two

Interesting facts

  • 1134308772 has 32 divisors, whose sum is 3150858600
  • The reverse of 1134308772 is 2778034311
  • Previous prime number is 9

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 36
  • Digital Root 9

Name

Name six hundred sixteen million seven hundred ninety-eight thousand three hundred thirty-seven

Interesting facts

  • 616798337 has 4 divisors, whose sum is 643615680
  • The reverse of 616798337 is 733897616
  • Previous prime number is 23

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 50
  • Digital Root 5