Find Amplitude, Period, and Phase Shift y=1/4cos(3pix)

Find Amplitude, Period, and Phase Shift y=1/4cos(3pix)
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 .
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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:
Cancel the common factor of and .
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Factor out of .
Phase Shift:
Cancel the common factors.
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Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Phase Shift:
Divide 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 seven hundred ninety-six million eight hundred twenty thousand three hundred forty-two

Interesting facts

  • 796820342 has 16 divisors, whose sum is 1237834752
  • The reverse of 796820342 is 243028697
  • Previous prime number is 307

Basic properties

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

Name

Name one billion eight hundred sixty-seven million one hundred seventy-two thousand four hundred five

Interesting facts

  • 1867172405 has 16 divisors, whose sum is 2579122560
  • The reverse of 1867172405 is 5042717681
  • Previous prime number is 7

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 41
  • Digital Root 5

Name

Name four hundred thirty-five million one hundred fourteen thousand forty-three

Interesting facts

  • 435114043 has 16 divisors, whose sum is 550002880
  • The reverse of 435114043 is 340411534
  • Previous prime number is 37

Basic properties

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