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>10</mn></mstyle></math>

Find the period of <math><mstyle displaystyle="true"><mn>10</mn><mi>sin</mi><mrow><mo>(</mo><mfrac><mrow><mn>3</mn><mi>π</mi><mi>x</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>3</mn><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>4</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><mn>3</mn><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> .

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

Cancel the common factor.

Rewrite the expression.

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

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"><mn>25</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><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> .

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

Cancel the common factor.

Rewrite the expression.

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

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><mn>3</mn><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>4</mn></mrow></mfrac></mrow><mrow><mfrac><mrow><mn>3</mn><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><mn>3</mn><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>4</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn><mi>π</mi></mrow></mfrac></mstyle></math>

Combine.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>2</mn></mrow><mrow><mn>4</mn><mrow><mo>(</mo><mn>3</mn><mi>π</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math>

Cancel the common factor of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Cancel the common factor.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><menclose notation="updiagonalstrike"><mn>3</mn></menclose><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>2</mn></mrow><mrow><mn>4</mn><mrow><mo>(</mo><menclose notation="updiagonalstrike"><mn>3</mn></menclose><mi>π</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math>

Rewrite the expression.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>2</mn></mrow><mrow><mn>4</mn><mrow><mo>(</mo><mi>π</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>2</mn></mrow><mrow><mn>4</mn><mrow><mo>(</mo><mi>π</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math>

Cancel the common factor of <math><mstyle displaystyle="true"><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> and <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"><msup><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>2</mn></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi><mrow><mo>(</mo><mi>π</mi><mo>⋅</mo><mn>2</mn><mo>)</mo></mrow></mrow><mrow><mn>4</mn><mrow><mo>(</mo><mi>π</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math>

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn><mrow><mo>(</mo><mi>π</mi><mo>)</mo></mrow></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi><mrow><mo>(</mo><mi>π</mi><mo>⋅</mo><mn>2</mn><mo>)</mo></mrow></mrow><mrow><mi>π</mi><mo>⋅</mo><mn>4</mn></mrow></mfrac></mstyle></math>

Cancel the common factor.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><menclose notation="updiagonalstrike"><mi>π</mi></menclose><mrow><mo>(</mo><mi>π</mi><mo>⋅</mo><mn>2</mn><mo>)</mo></mrow></mrow><mrow><menclose notation="updiagonalstrike"><mi>π</mi></menclose><mo>⋅</mo><mn>4</mn></mrow></mfrac></mstyle></math>

Rewrite the expression.

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

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

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

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

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

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

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

List the properties of the trigonometric function.

Amplitude: <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math>

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

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> to the right)

Vertical Shift: <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math>

Do you know how to Find Amplitude, Period, and Phase Shift y=10sin((6pi)/4(x-pi/2))+25? 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 thirty-five million nine hundred sixty-five thousand one hundred seventy-two |
---|

- 1235965172 has 32 divisors, whose sum is
**3067888824** - The reverse of 1235965172 is
**2715695321** - Previous prime number is
**41**

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

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

- 1904577038 has 64 divisors, whose sum is
**3576545280** - The reverse of 1904577038 is
**8307754091** - Previous prime number is
**383**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 44
- Digital Root 8

Name | one billion nineteen million seven hundred eighty-six thousand six hundred eighty-one |
---|

- 1019786681 has 4 divisors, whose sum is
**1019872500** - The reverse of 1019786681 is
**1866879101** - Previous prime number is
**14249**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 47
- Digital Root 2