Find Amplitude, Period, and Phase Shift y=1/2*cos(4x-(2pi)/3)

Find Amplitude, Period, and Phase Shift y=1/2*cos(4x-(2pi)/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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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 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:
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:
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:
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 million three hundred thirty-two thousand five hundred

Interesting facts

  • 1002332500 has 128 divisors, whose sum is 3637382112
  • The reverse of 1002332500 is 0052332001
  • 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 two billion one hundred thirty million three hundred fifty-three thousand six hundred ninety-two

Interesting facts

  • 2130353692 has 16 divisors, whose sum is 4806149832
  • The reverse of 2130353692 is 2963530312
  • Previous prime number is 373

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 34
  • Digital Root 7

Name

Name three hundred eight million fifteen thousand three hundred sixty-eight

Interesting facts

  • 308015368 has 16 divisors, whose sum is 1039551894
  • The reverse of 308015368 is 863510803
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 34
  • Digital Root 7