Rewrite the expression as <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mi>sin</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi><mi>x</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>)</mo></mrow><mo>-</mo><mn>2</mn></mstyle></math> .

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>

Find the period of <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mi>sin</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi><mi>x</mi></mrow><mrow><mn>2</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><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><mi>π</mi></mrow><mrow><mn>2</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"><mi>π</mi></mstyle></math> .

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

Cancel the common factor.

Rewrite the expression.

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

Find the period of <math><mstyle displaystyle="true"><mo>-</mo><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><mi>π</mi></mrow><mrow><mn>2</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"><mi>π</mi></mstyle></math> .

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

Cancel the common factor.

Rewrite the expression.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></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><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mrow><mrow><mfrac><mrow><mi>π</mi></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"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math>

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

Cancel the common factor.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><menclose notation="updiagonalstrike"><mi>π</mi></menclose></mrow><mrow><mn>6</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>2</mn></mrow><mrow><menclose notation="updiagonalstrike"><mi>π</mi></menclose></mrow></mfrac></mstyle></math>

Rewrite the expression.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>⋅</mo><mn>2</mn></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>⋅</mo><mn>2</mn></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>6</mn></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></mfrac><mo>⋅</mo><mn>2</mn></mstyle></math>

Cancel the common factor.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><menclose notation="updiagonalstrike"><mn>2</mn></menclose><mo>⋅</mo><mn>3</mn></mrow></mfrac><mo>⋅</mo><menclose notation="updiagonalstrike"><mn>2</mn></menclose></mstyle></math>

Rewrite the expression.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</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"><mn>4</mn></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> to the right)

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

Do you know how to Find Amplitude, Period, and Phase Shift y=-2-4sin(pi/2(x-1/3))? 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 nine hundred seventy-four million nine hundred fifty-five thousand two hundred sixty-nine |
---|

- 1974955269 has 8 divisors, whose sum is
**2089090432** - The reverse of 1974955269 is
**9625594791** - Previous prime number is
**103**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 57
- Digital Root 3

Name | one billion eight hundred forty-four million seventy-nine thousand eight hundred thirty-eight |
---|

- 1844079838 has 8 divisors, whose sum is
**2781573480** - The reverse of 1844079838 is
**8389704481** - Previous prime number is
**179**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 52
- Digital Root 7

Name | five hundred thirty-three million nine hundred fifty-eight thousand eight hundred sixteen |
---|

- 533958816 has 128 divisors, whose sum is
**5406333984** - The reverse of 533958816 is
**618859335** - Previous prime number is
**3**

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