Find Amplitude, Period, and Phase Shift y=2cot(1/3x+pi/6)+2

Find Amplitude, Period, and Phase Shift y=2cot(1/3x+pi/6)+2
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Since the graph of the function does not have a maximum or minimum value, there can be no value for the amplitude.
Amplitude: None
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.
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Move to the left of .
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.
Move to the left of .
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:
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:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Move the negative in front of the fraction.
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude: None
Period:
Phase Shift: ( to the left)
Vertical Shift:
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Name

Name one billion one hundred eleven million five hundred seventy-one thousand four hundred twenty-six

Interesting facts

  • 1111571426 has 16 divisors, whose sum is 1923362496
  • The reverse of 1111571426 is 6241751111
  • Previous prime number is 107

Basic properties

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

Name

Name eight hundred sixteen million nine hundred forty-nine thousand two hundred ninety-nine

Interesting facts

  • 816949299 has 4 divisors, whose sum is 1089265736
  • The reverse of 816949299 is 992949618
  • Previous prime number is 3

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 9
  • Sum of Digits 57
  • Digital Root 3

Name

Name one billion four hundred million one hundred twenty-four thousand six hundred twenty-seven

Interesting facts

  • 1400124627 has 16 divisors, whose sum is 2715393408
  • The reverse of 1400124627 is 7264210041
  • Previous prime number is 11

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 27
  • Digital Root 9