Use the form <math><mstyle displaystyle="true"><mi>a</mi><mi>cot</mi><mrow><mo>(</mo><mi>b</mi><mi>x</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow><mo>+</mo><mi>d</mi></mstyle></math> to find the variables used to find the amplitude, period, phase shift, and vertical shift.

Since the graph of the function <math><mstyle displaystyle="true"><mi>c</mi><mi>o</mi><mi>t</mi></mstyle></math> does not have a maximum or minimum value, there can be no value for the amplitude.

Amplitude: None

Find the period of <math><mstyle displaystyle="true"><mn>2</mn><mi>cot</mi><mrow><mo>(</mo><mfrac><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mrow><mo>|</mo><mi>b</mi><mo>|</mo></mrow></mrow></mfrac></mstyle></math> .

Replace <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> with <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> in the formula for period.

Multiply the numerator by the reciprocal of the denominator.

Move <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Find the period of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mrow><mo>|</mo><mi>b</mi><mo>|</mo></mrow></mrow></mfrac></mstyle></math> .

Replace <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> with <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> in the formula for period.

Multiply the numerator by the reciprocal of the denominator.

Move <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

The period of addition/subtraction of trig functions is the maximum of the individual periods.

The phase shift of the function can be calculated from <math><mstyle displaystyle="true"><mfrac><mrow><mi>c</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>c</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math>

Replace the values of <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> in the equation for phase shift.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></mfrac></mstyle></math>

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>⋅</mo><mn>3</mn></mstyle></math>

Cancel the common factor of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Move the leading negative in <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> into the numerator.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>⋅</mo><mn>3</mn></mstyle></math>

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mi>π</mi></mrow><mrow><mn>3</mn><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mrow></mfrac><mo>⋅</mo><mn>3</mn></mstyle></math>

Cancel the common factor.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mi>π</mi></mrow><mrow><menclose notation="updiagonalstrike"><mn>3</mn></menclose><mo>⋅</mo><mn>2</mn></mrow></mfrac><mo>⋅</mo><menclose notation="updiagonalstrike"><mn>3</mn></menclose></mstyle></math>

Rewrite the expression.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>

Move the negative in front of the fraction.

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>

List the properties of the trigonometric function.

Amplitude: None

Period: <math><mstyle displaystyle="true"><mn>3</mn><mi>π</mi></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> to the left)

Vertical Shift: <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math>

Do you know how to Find Amplitude, Period, and Phase Shift y=2cot(1/3x+pi/6)+2? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | three hundred ninety-five million five hundred fifty-eight thousand two hundred six |
---|

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

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

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

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

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

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

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

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