Find Amplitude, Period, and Phase Shift y=2cos(4x+pi)-3

Find Amplitude, Period, and Phase Shift y=2cos(4x+pi)-3
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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Find the period of .
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The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
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.
Find the period of .
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The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
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.
The period of addition/subtraction of trig functions is the maximum of the individual periods.
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:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the left)
Vertical Shift:
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Name

Name one billion five hundred eighteen million one hundred sixty-eight thousand two hundred ninety-seven

Interesting facts

  • 1518168297 has 4 divisors, whose sum is 2024224400
  • The reverse of 1518168297 is 7928618151
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 48
  • Digital Root 3

Name

Name six hundred seventy-five million seven hundred eighteen thousand seventy-six

Interesting facts

  • 675718076 has 32 divisors, whose sum is 1543686768
  • The reverse of 675718076 is 670817576
  • Previous prime number is 73

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 47
  • Digital Root 2

Name

Name one billion three hundred ten million eight hundred eighty-one thousand two hundred fourteen

Interesting facts

  • 1310881214 has 16 divisors, whose sum is 2020453008
  • The reverse of 1310881214 is 4121880131
  • Previous prime number is 37

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 29
  • Digital Root 2