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>2</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>8</mn><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> in the formula for period.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mn>8</mn><mi>π</mi></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

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>3</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mfrac><mrow><mn>8</mn><mi>π</mi></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><mn>3</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>8</mn><mi>π</mi></mrow></mfrac></mstyle></math>

Cancel the common factor of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Move the leading negative in <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> into the numerator.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>3</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>8</mn><mi>π</mi></mrow></mfrac></mstyle></math>

Factor <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><mi>π</mi></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi><mo>⋅</mo><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>8</mn><mi>π</mi></mrow></mfrac></mstyle></math>

Factor <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mn>8</mn><mi>π</mi></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi><mo>⋅</mo><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mi>π</mi><mo>⋅</mo><mn>8</mn></mrow></mfrac></mstyle></math>

Cancel the common factor.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><menclose notation="updiagonalstrike"><mi>π</mi></menclose><mo>⋅</mo><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>3</mn></mrow><mrow><menclose notation="updiagonalstrike"><mi>π</mi></menclose><mo>⋅</mo><mn>8</mn></mrow></mfrac></mstyle></math>

Rewrite the expression.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>8</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>8</mn></mrow></mfrac></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>8</mn></mrow></mfrac></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>⋅</mo><mn>3</mn></mrow><mrow><mn>2</mn><mo>⋅</mo><mn>8</mn></mrow></mfrac></mstyle></math>

Simplify the expression.

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

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>9</mn></mrow><mrow><mn>2</mn><mo>⋅</mo><mn>8</mn></mrow></mfrac></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>9</mn></mrow><mrow><mn>16</mn></mrow></mfrac></mstyle></math>

Move the negative in front of the fraction.

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>9</mn></mrow><mrow><mn>16</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>9</mn></mrow><mrow><mn>16</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>9</mn></mrow><mrow><mn>16</mn></mrow></mfrac></mstyle></math>

List the properties of the trigonometric function.

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

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

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>9</mn></mrow><mrow><mn>16</mn></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mn>9</mn></mrow><mrow><mn>16</mn></mrow></mfrac></mstyle></math> to the left)

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=2sin((8pix)/3+(3pi)/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 | one billion seven hundred four million six hundred fifteen thousand six hundred eighteen |
---|

- 1704615618 has 8 divisors, whose sum is
**3409231248** - The reverse of 1704615618 is
**8165164071** - Previous prime number is
**3**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 39
- Digital Root 3

Name | one billion two hundred seventy million seven hundred fifty-seven thousand eight hundred ninety-seven |
---|

- 1270757897 has 4 divisors, whose sum is
**1286843520** - The reverse of 1270757897 is
**7987570721** - Previous prime number is
**79**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 53
- Digital Root 8

Name | one billion two hundred eighty-seven million two hundred sixty-two thousand five hundred thirty-five |
---|

- 1287262535 has 16 divisors, whose sum is
**1665002304** - The reverse of 1287262535 is
**5352627821** - Previous prime number is
**1223**

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