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"><mn>100</mn></mstyle></math> in the formula for period.

The absolute value is the distance between a number and zero. The distance between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>100</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>100</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>100</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>100</mn></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><mo>-</mo><mn>1</mn></mrow><mrow><mn>100</mn></mrow></mfrac></mstyle></math>

Move the negative in front of the fraction.

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>100</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>100</mn></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"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>50</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>100</mn></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>100</mn></mrow></mfrac></mstyle></math> to the left)

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=3sin(100x+1)? 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 | three hundred eighty-four million ninety-seven thousand thirty |
---|

- 384097030 has 16 divisors, whose sum is
**693949680** - The reverse of 384097030 is
**030790483** - Previous prime number is
**269**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 34
- Digital Root 7

Name | six hundred sixty-six million eighty-three thousand seven hundred |
---|

- 666083700 has 64 divisors, whose sum is
**1736017920** - The reverse of 666083700 is
**007380666** - Previous prime number is
**643**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 36
- Digital Root 9

Name | one billion four hundred ten million six hundred twenty thousand nine hundred seventy-six |
---|

- 1410620976 has 64 divisors, whose sum is
**7934743800** - The reverse of 1410620976 is
**6790260141** - Previous prime number is
**9**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 36
- Digital Root 9