Find Amplitude, Period, and Phase Shift f(t)=25sin(160pit)+115

Find Amplitude, Period, and Phase Shift f(t)=25sin(160pit)+115
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 and .
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Factor out of .
Period:
Cancel the common factors.
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Factor out of .
Period:
Cancel the common factor.
Period:
Rewrite the expression.
Period:
Period:
Period:
Cancel the common factor of .
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Cancel the common factor.
Period:
Rewrite the expression.
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:
Cancel the common factor of and .
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Factor out of .
Phase Shift:
Cancel the common factors.
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Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Phase Shift:
Divide by .
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 two hundred million three hundred thirty-three thousand forty

Interesting facts

  • 1200333040 has 64 divisors, whose sum is 7292023704
  • The reverse of 1200333040 is 0403330021
  • Previous prime number is 5

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 16
  • Digital Root 7

Name

Name one billion two hundred seventy-seven million one hundred thirty-nine thousand nine hundred fifty-five

Interesting facts

  • 1277139955 has 32 divisors, whose sum is 1591783424
  • The reverse of 1277139955 is 5599317721
  • Previous prime number is 223

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 49
  • Digital Root 4

Name

Name seven million seven hundred forty-two thousand six hundred twenty-four

Interesting facts

  • 7742624 has 128 divisors, whose sum is 59276448
  • The reverse of 7742624 is 4262477
  • Previous prime number is 131

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 7
  • Sum of Digits 32
  • Digital Root 5