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 eight hundred eighty-one million one hundred three thousand nine hundred eighty-seven

Interesting facts

  • 881103987 has 32 divisors, whose sum is 1326624768
  • The reverse of 881103987 is 789301188
  • Previous prime number is 23

Basic properties

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

Name

Name one billion six hundred thirty-one million seventy-six thousand four hundred fifty-two

Interesting facts

  • 1631076452 has 16 divisors, whose sum is 3692438352
  • The reverse of 1631076452 is 2546701361
  • Previous prime number is 163

Basic properties

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

Name

Name one billion fifty million fifty-three thousand four hundred four

Interesting facts

  • 1050053404 has 16 divisors, whose sum is 2383529328
  • The reverse of 1050053404 is 4043500501
  • Previous prime number is 113

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 22
  • Digital Root 4