Find Amplitude, Period, and Phase Shift y=-1/2*cos(pix-pi/18)

Find Amplitude, Period, and Phase Shift y=-1/2*cos(pix-pi/18)
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 using the formula .
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The period of the function can be calculated using .
Period:
Replace with in the formula for period.
Period:
Solve the equation.
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is approximately which is positive so remove the absolute value
Period:
Cancel the common factor of .
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Cancel the common factor.
Period:
Divide by .
Period:
Period:
Period:
Period:
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:
Cancel the common factor of .
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Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Phase Shift:
Find the vertical shift .
Vertical Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the right)
Vertical Shift:
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Name

Name one billion four hundred eighty-two million seven hundred fifty-one thousand one hundred forty-eight

Interesting facts

  • 1482751148 has 8 divisors, whose sum is 3336190092
  • The reverse of 1482751148 is 8411572841
  • Previous prime number is 2

Basic properties

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

Name

Name eight hundred four million two hundred seventy thousand nine hundred forty-two

Interesting facts

  • 804270942 has 32 divisors, whose sum is 2147534208
  • The reverse of 804270942 is 249072408
  • Previous prime number is 773

Basic properties

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

Name

Name three hundred twenty-six million two hundred fifty-four thousand four hundred forty-six

Interesting facts

  • 326254446 has 64 divisors, whose sum is 689420160
  • The reverse of 326254446 is 644452623
  • Previous prime number is 7

Basic properties

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