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>3</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"><mi>π</mi></mstyle></math> in the formula for period.

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

Cancel the common factor.

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

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>π</mi></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>π</mi></mrow></mfrac></mstyle></math>

List the properties of the trigonometric function.

Amplitude: <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math>

Period: <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>π</mi></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>π</mi></mrow></mfrac></mstyle></math> to the right)

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=3sin(pix-1/2)? 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 four hundred forty-one million eight hundred sixty-nine thousand four hundred seventy-five |
---|

- 1441869475 has 16 divisors, whose sum is
**2089035936** - The reverse of 1441869475 is
**5749681441** - Previous prime number is
**163**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 49
- Digital Root 4

Name | three hundred sixty-eight million four hundred thirty-eight thousand eight hundred fifty-three |
---|

- 368438853 has 8 divisors, whose sum is
**492162016** - The reverse of 368438853 is
**358834863** - Previous prime number is
**541**

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

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

- 1696805296 has 32 divisors, whose sum is
**8590076892** - The reverse of 1696805296 is
**6925086961** - Previous prime number is
**2**

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