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 one billion one hundred fifty-one million two hundred thirty-eight thousand eight hundred six

Interesting facts

  • 1151238806 has 4 divisors, whose sum is 1726858212
  • The reverse of 1151238806 is 6088321511
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 35
  • Digital Root 8

Name

Name eight hundred seventy-six million four hundred sixteen thousand five hundred fourteen

Interesting facts

  • 876416514 has 16 divisors, whose sum is 1753754880
  • The reverse of 876416514 is 415614678
  • Previous prime number is 1951

Basic properties

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

Name

Name seven hundred eighty-two million nine hundred fifty-two thousand one hundred ninety

Interesting facts

  • 782952190 has 16 divisors, whose sum is 1218877056
  • The reverse of 782952190 is 091259287
  • Previous prime number is 37

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 43
  • Digital Root 7