Find Amplitude, Period, and Phase Shift f(x)=-4sin(2x+pi)-5

Find Amplitude, Period, and Phase Shift f(x)=-4sin(2x+pi)-5
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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The absolute value is the distance between a number and zero. The distance between and is .
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:
Move the negative in front of the fraction.
Phase Shift:
Phase Shift:
Find the vertical shift .
Vertical Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the left)
Vertical Shift:
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Name

Name one hundred thirty-one million three hundred ninety-one thousand nine hundred forty

Interesting facts

  • 131391940 has 32 divisors, whose sum is 355155840
  • The reverse of 131391940 is 049193131
  • Previous prime number is 1039

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 31
  • Digital Root 4

Name

Name one billion eight hundred seventy-two million nine hundred seventy-two thousand six hundred fourteen

Interesting facts

  • 1872972614 has 32 divisors, whose sum is 2989980000
  • The reverse of 1872972614 is 4162792781
  • Previous prime number is 293

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 47
  • Digital Root 2

Name

Name one billion seventy-four million one hundred twenty-one thousand fifty-six

Interesting facts

  • 1074121056 has 256 divisors, whose sum is 14500638144
  • The reverse of 1074121056 is 6501214701
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 27
  • Digital Root 9