Find Amplitude, Period, and Phase Shift y=4sin(2/3x+pi/9)

Find Amplitude, Period, and Phase Shift y=4sin(2/3x+pi/9)
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:
Cancel the common factor of .
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Move the leading negative in into the numerator.
Phase Shift:
Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Multiply and .
Phase Shift:
Simplify the expression.
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Multiply by .
Phase Shift:
Move the negative in front of the fraction.
Phase Shift:
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 three hundred seventy-nine million five hundred fifty-one thousand three hundred eighty-eight

Interesting facts

  • 379551388 has 8 divisors, whose sum is 853990632
  • The reverse of 379551388 is 883155973
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 49
  • Digital Root 4

Name

Name eight hundred twenty-five million nine hundred seventy-eight thousand eight hundred ninety-one

Interesting facts

  • 825978891 has 16 divisors, whose sum is 1123430400
  • The reverse of 825978891 is 198879528
  • Previous prime number is 79

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 57
  • Digital Root 3

Name

Name two hundred seventy-four million eight hundred fifty-one thousand two hundred twenty-five

Interesting facts

  • 274851225 has 16 divisors, whose sum is 290437952
  • The reverse of 274851225 is 522158472
  • Previous prime number is 297

Basic properties

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