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>5</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> .

Period: <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>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> in the formula for period.

Period: <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mrow><mo>|</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>|</mo></mrow></mrow></mfrac></mstyle></math>

Solve the equation.

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

Multiply the numerator by the reciprocal of the denominator.

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

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

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

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

Cancel the common factor.

Period: <math><mstyle displaystyle="true"><menclose notation="updiagonalstrike"><mn>2</mn></menclose><mi>π</mi><mrow><mo>(</mo><mfrac><mrow><mn>3</mn></mrow><mrow><menclose notation="updiagonalstrike"><mn>2</mn></menclose></mrow></mfrac><mo>)</mo></mrow></mstyle></math>

Rewrite the expression.

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

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

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

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

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

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

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

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

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

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

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></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: <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math>

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

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></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 y=5sin((2x)/3-pi)? 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 hundred eighty-two million one hundred forty-seven thousand eight hundred thirty-four |
---|

- 182147834 has 32 divisors, whose sum is
**326140992** - The reverse of 182147834 is
**438741281** - Previous prime number is
**401**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 38
- Digital Root 2

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

- 1655022208 has 2048 divisors, whose sum is
**34549701120** - The reverse of 1655022208 is
**8022205561** - Previous prime number is
**67**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 31
- Digital Root 4

Name | one billion eight hundred twenty-two million four hundred sixteen thousand seven hundred five |
---|

- 1822416705 has 16 divisors, whose sum is
**2167578880** - The reverse of 1822416705 is
**5076142281** - Previous prime number is
**283**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 36
- Digital Root 9