Find Amplitude, Period, and Phase Shift y=cos((xpi)/3)

Find Amplitude, Period, and Phase Shift y=cos((xpi)/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
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
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 by .
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: None
Vertical Shift: None
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Name

Name one billion nine hundred seventy-one million eight hundred forty-one thousand four hundred twenty-eight

Interesting facts

  • 1971841428 has 128 divisors, whose sum is 5132574720
  • The reverse of 1971841428 is 8241481791
  • Previous prime number is 31

Basic properties

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

Name

Name one billion three hundred thirty-two million four hundred twelve thousand six hundred ninety-seven

Interesting facts

  • 1332412697 has 8 divisors, whose sum is 1661189952
  • The reverse of 1332412697 is 7962142331
  • Previous prime number is 7

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 38
  • Digital Root 2

Name

Name four hundred eighty-five million two hundred eleven thousand seven hundred seventy-three

Interesting facts

  • 485211773 has 8 divisors, whose sum is 517158720
  • The reverse of 485211773 is 377112584
  • Previous prime number is 17

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 38
  • Digital Root 2