Find Amplitude, Period, and Phase Shift y=1/4sin(8pix-(5pi)/4)

Find Amplitude, Period, and Phase Shift y=1/4sin(8pix-(5pi)/4)
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 and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
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:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Cancel the common factor of .
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Factor out of .
Phase Shift:
Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Multiply and .
Phase Shift:
Multiply by .
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the right)
Vertical Shift: None
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Name

Name one billion seventy-one million five hundred eleven thousand three hundred thirty-nine

Interesting facts

  • 1071511339 has 4 divisors, whose sum is 1086603120
  • The reverse of 1071511339 is 9331151701
  • Previous prime number is 71

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 31
  • Digital Root 4

Name

Name four hundred twenty-nine million five hundred seven thousand six hundred sixty-nine

Interesting facts

  • 429507669 has 16 divisors, whose sum is 447720000
  • The reverse of 429507669 is 966705924
  • Previous prime number is 349

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 48
  • Digital Root 3

Name

Name one billion seven hundred thirteen million ninety-seven thousand two hundred eleven

Interesting facts

  • 1713097211 has 8 divisors, whose sum is 1958208000
  • The reverse of 1713097211 is 1127903171
  • Previous prime number is 5827

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 32
  • Digital Root 5