Find Amplitude, Period, and Phase Shift y=3cos((2x)/3+3pi)

Find Amplitude, Period, and Phase Shift y=3cos((2x)/3+3pi)
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.
Move to the left of .
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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Combine and .
Phase Shift:
Multiply by .
Phase Shift:
Combine and .
Phase Shift:
Phase Shift:
Move the negative in front of the fraction.
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the left)
Vertical Shift: None
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Name

Name one billion two hundred eighty-eight million ninety-one thousand nine hundred seventy-nine

Interesting facts

  • 1288091979 has 8 divisors, whose sum is 1431612000
  • The reverse of 1288091979 is 9791908821
  • Previous prime number is 3989

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 54
  • Digital Root 9

Name

Name one billion nine hundred twenty-four million one hundred thirty thousand eight hundred eighty-five

Interesting facts

  • 1924130885 has 16 divisors, whose sum is 2391316992
  • The reverse of 1924130885 is 5880314291
  • Previous prime number is 71

Basic properties

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

Name

Name two billion one hundred seventeen million eight hundred sixty-five thousand one hundred sixty-nine

Interesting facts

  • 2117865169 has 8 divisors, whose sum is 2422122560
  • The reverse of 2117865169 is 9615687112
  • Previous prime number is 1429

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 46
  • Digital Root 1