Use the form <math><mstyle displaystyle="true"><mi>a</mi><mi>tan</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>t</mi><mi>a</mi><mi>n</mi></mstyle></math> does not have a maximum or minimum value, there can be no value for the amplitude.

Amplitude: None

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> .

Period: <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>2</mn></mrow></mfrac></mstyle></math> in the formula for period.

Period: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mrow><mo>|</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>|</mo></mrow></mrow></mfrac></mstyle></math>

Solve the equation.

Period: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mfrac></mstyle></math>

Multiply the numerator by the reciprocal of the denominator.

Period: <math><mstyle displaystyle="true"><mi>π</mi><mo>⋅</mo><mn>2</mn></mstyle></math>

Move <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Period: <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math>

Period: <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math>

Period: <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math>

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><mn>0</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mfrac></mstyle></math>

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: <math><mstyle displaystyle="true"><mn>0</mn><mo>⋅</mo><mn>2</mn></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math>

Find the vertical shift <math><mstyle displaystyle="true"><mi>d</mi></mstyle></math> .

Vertical Shift: <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math>

List the properties of the trigonometric function.

Amplitude: None

Period: <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> (<math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> to the right)

Vertical Shift: <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math>

Do you know how to Find Amplitude, Period, and Phase Shift f(x)=tan(x/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 | four hundred ninety-one million three hundred fifty-eight thousand four hundred ninety-five |
---|

- 491358495 has 32 divisors, whose sum is
**803639232** - The reverse of 491358495 is
**594853194** - Previous prime number is
**373**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 48
- Digital Root 3

Name | one billion nine hundred two million nine hundred forty-four thousand five hundred seventy-one |
---|

- 1902944571 has 4 divisors, whose sum is
**1960609592** - The reverse of 1902944571 is
**1754492091** - Previous prime number is
**33**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 42
- Digital Root 6

Name | eight hundred twenty-six million three hundred sixty-nine thousand one hundred ten |
---|

- 826369110 has 64 divisors, whose sum is
**2117016000** - The reverse of 826369110 is
**011963628** - Previous prime number is
**53**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 36
- Digital Root 9