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"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></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"><mn>8</mn><mi>π</mi></mstyle></math> in the formula for period.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>8</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> .

Cancel the common factors.

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

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of <math><mstyle displaystyle="true"><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><mfrac><mrow><mn>5</mn><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mrow><mrow><mn>8</mn><mi>π</mi></mrow></mfrac></mstyle></math>

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</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> .

Factor <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mn>5</mn><mi>π</mi></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi><mo>⋅</mo><mn>5</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</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><mn>5</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</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><mn>5</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</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><mn>5</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>8</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>8</mn></mrow></mfrac></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>8</mn></mrow></mfrac></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><mn>4</mn><mo>⋅</mo><mn>8</mn></mrow></mfrac></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><mn>32</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><mn>32</mn></mrow></mfrac></mstyle></math>

List the properties of the trigonometric function.

Amplitude: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>

Period: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><mn>32</mn></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><mn>32</mn></mrow></mfrac></mstyle></math> to the right)

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=1/4sin(8pix-(5pi)/4)? 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 seventy-one million five hundred eleven thousand three hundred thirty-nine |
---|

- 1071511339 has 4 divisors, whose sum is
**1086603120** - The reverse of 1071511339 is
**9331151701** - Previous prime number is
**71**

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

Name | four hundred twenty-nine million five hundred seven thousand six hundred sixty-nine |
---|

- 429507669 has 16 divisors, whose sum is
**447720000** - The reverse of 429507669 is
**966705924** - Previous prime number is
**349**

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

Name | one billion seven hundred thirteen million ninety-seven thousand two hundred eleven |
---|

- 1713097211 has 8 divisors, whose sum is
**1958208000** - The reverse of 1713097211 is
**1127903171** - Previous prime number is
**5827**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 32
- Digital Root 5