Find Amplitude, Period, and Phase Shift y=cos(6pix+pi/2)

Find Amplitude, Period, and Phase Shift y=cos(6pix+pi/2)
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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Move the leading negative in into the numerator.
Phase Shift:
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:
Simplify the expression.
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Multiply by .
Phase Shift:
Move the negative in front of the fraction.
Phase Shift:
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the left)
Vertical Shift: None
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Name

Name one billion seven hundred fifty-one million one hundred eighty-nine thousand five hundred twelve

Interesting facts

  • 1751189512 has 32 divisors, whose sum is 5922616320
  • The reverse of 1751189512 is 2159811571
  • Previous prime number is 479

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 40
  • Digital Root 4

Name

Name seven hundred sixty-three million eight hundred nineteen thousand one hundred fifty-five

Interesting facts

  • 763819155 has 64 divisors, whose sum is 1221350400
  • The reverse of 763819155 is 551918367
  • Previous prime number is 151

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 45
  • Digital Root 9

Name

Name two hundred ninety-four million one hundred twenty-five thousand nine hundred sixty-six

Interesting facts

  • 294125966 has 8 divisors, whose sum is 464409480
  • The reverse of 294125966 is 669521492
  • Previous prime number is 19

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 44
  • Digital Root 8