Use the form <math><mstyle displaystyle="true"><mi>a</mi><mi>sin</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.

Find the amplitude <math><mstyle displaystyle="true"><mrow><mo>|</mo><mi>a</mi><mo>|</mo></mrow></mstyle></math> .

Amplitude: <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math>

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><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>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> in the formula for period.

Multiply the numerator by the reciprocal of the denominator.

Multiply <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><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><mo>-</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow><mrow><mfrac><mrow><mn>3</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"><mo>-</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>2</mn><mo>⋅</mo><mn>4</mn></mrow><mrow><mn>3</mn><mo>⋅</mo><mn>3</mn></mrow></mfrac></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>8</mn></mrow><mrow><mn>3</mn><mo>⋅</mo><mn>3</mn></mrow></mfrac></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>8</mn></mrow><mrow><mn>9</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>8</mn></mrow><mrow><mn>9</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>8</mn></mrow><mrow><mn>9</mn></mrow></mfrac></mstyle></math>

List the properties of the trigonometric function.

Amplitude: <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math>

Period: <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>8</mn></mrow><mrow><mn>9</mn></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mn>8</mn></mrow><mrow><mn>9</mn></mrow></mfrac></mstyle></math> to the left)

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=4sin((3x)/2+4/3)? 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 | one billion two hundred forty-nine million five hundred thirty-nine thousand fifty-five |
---|

- 1249539055 has 8 divisors, whose sum is
**1564640352** - The reverse of 1249539055 is
**5509359421** - Previous prime number is
**23**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 43
- Digital Root 7

Name | one billion eighty-five million twenty-eight thousand seven hundred fifty-six |
---|

- 1085028756 has 32 divisors, whose sum is
**2517927552** - The reverse of 1085028756 is
**6578205801** - Previous prime number is
**41**

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

Name | one billion five hundred seventy million six hundred six thousand six hundred fifty-six |
---|

- 1570606656 has 512 divisors, whose sum is
**23900725728** - The reverse of 1570606656 is
**6566060751** - Previous prime number is
**523**

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