Find Amplitude, Period, and Phase Shift y=10cos((2pi)/3(x+1/4))

Find Amplitude, Period, and Phase Shift y=10cos((2pi)/3(x+1/4))
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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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:
Cancel the common factor of .
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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 hundred seventy-six million six hundred forty-eight thousand seven hundred thirty-one

Interesting facts

  • 176648731 has 8 divisors, whose sum is 202026240
  • The reverse of 176648731 is 137846671
  • Previous prime number is 1559

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 43
  • Digital Root 7

Name

Name eight hundred ninety-five million nine hundred forty-eight thousand five hundred fifty-seven

Interesting facts

  • 895948557 has 8 divisors, whose sum is 947387232
  • The reverse of 895948557 is 755849598
  • Previous prime number is 107

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 60
  • Digital Root 6

Name

Name one billion seven million one hundred ninety-four thousand sixty-two

Interesting facts

  • 1007194062 has 16 divisors, whose sum is 2302157952
  • The reverse of 1007194062 is 2604917001
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 30
  • Digital Root 3