Find Amplitude, Period, and Phase Shift y=cos((6pix)/5+pi/3)

Find Amplitude, Period, and Phase Shift y=cos((6pix)/5+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 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
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
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Factor out of .
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:
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 six hundred thirty-one million three hundred eighty-two thousand eight hundred seventy-six

Interesting facts

  • 631382876 has 16 divisors, whose sum is 1428824664
  • The reverse of 631382876 is 678283136
  • Previous prime number is 173

Basic properties

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

Name

Name nine hundred sixty-nine million seven hundred fifty-two thousand six hundred two

Interesting facts

  • 969752602 has 16 divisors, whose sum is 1573751592
  • The reverse of 969752602 is 206257969
  • Previous prime number is 13

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 46
  • Digital Root 1

Name

Name one billion five hundred sixty-nine million five hundred forty-seven thousand five hundred seventeen

Interesting facts

  • 1569547517 has 8 divisors, whose sum is 1579708416
  • The reverse of 1569547517 is 7157459651
  • Previous prime number is 2287

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 50
  • Digital Root 5