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>1</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>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> in the formula for period.

Multiply the numerator by the reciprocal of the denominator.

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></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><mfrac><mrow><mi>π</mi></mrow><mrow><mn>18</mn></mrow></mfrac></mrow><mrow><mfrac><mrow><mn>1</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"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>18</mn></mrow></mfrac><mo>⋅</mo><mn>3</mn></mstyle></math>

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

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>18</mn></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mrow></mfrac><mo>⋅</mo><mn>3</mn></mstyle></math>

Cancel the common factor.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><menclose notation="updiagonalstrike"><mn>3</mn></menclose><mo>⋅</mo><mn>6</mn></mrow></mfrac><mo>⋅</mo><menclose notation="updiagonalstrike"><mn>3</mn></menclose></mstyle></math>

Rewrite the expression.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math>

List the properties of the trigonometric function.

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

Period: <math><mstyle displaystyle="true"><mn>6</mn><mi>π</mi></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> to the right)

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=sin(1/3(x-pi/6))? 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 three hundred seventy million six hundred sixty-two thousand four hundred forty-one |
---|

- 1370662441 has 4 divisors, whose sum is
**1371917572** - The reverse of 1370662441 is
**1442660731** - Previous prime number is
**1093**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 34
- Digital Root 7

Name | nine hundred ninety-one million ninety-eight thousand two hundred fifty-five |
---|

- 991098255 has 8 divisors, whose sum is
**994165248** - The reverse of 991098255 is
**552890199** - Previous prime number is
**1051**

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

Name | four hundred ninety-five million eight hundred eighty-nine thousand four hundred fifty-eight |
---|

- 495889458 has 16 divisors, whose sum is
**994592736** - The reverse of 495889458 is
**854988594** - Previous prime number is
**353**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 60
- Digital Root 6