# 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 .
Find the period of .
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 .
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 .
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 .
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 three hundred ninety-five million five hundred fifty-eight thousand two hundred six

### Interesting facts

• 395558206 has 4 divisors, whose sum is 593337312
• The reverse of 395558206 is 602855593
• Previous prime number is 2

### Basic properties

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

### Name

Name one billion three hundred seventy-five million six hundred twenty-one thousand six hundred twenty-eight

### Interesting facts

• 1375621628 has 16 divisors, whose sum is 3096868464
• The reverse of 1375621628 is 8261265731
• Previous prime number is 1817

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 41
• Digital Root 5

### Name

Name six hundred forty-one million two hundred fifty-six thousand five hundred thirty-five

### Interesting facts

• 641256535 has 8 divisors, whose sum is 769998096
• The reverse of 641256535 is 535652146
• Previous prime number is 1601

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 37
• Digital Root 1