Use the form <math><mstyle displaystyle="true"><mi>a</mi><mi>sin</mi><mrow><mo>(</mo><mi>b</mi><mi>θ</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>

Find the period of <math><mstyle displaystyle="true"><mn>3</mn><mi>sin</mi><mrow><mo>(</mo><mfrac><mrow><mi>θ</mi></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>1</mn></mrow><mrow><mn>4</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>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Find the period of <math><mstyle displaystyle="true"><mo>-</mo><mn>2</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>4</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>4</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><mn>0</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfrac></mstyle></math>

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: <math><mstyle displaystyle="true"><mn>0</mn><mo>⋅</mo><mn>4</mn></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mn>0</mn></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>8</mn><mi>π</mi></mstyle></math>

Phase Shift: None

Vertical Shift: <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math>

Do you know how to Find Amplitude, Period, and Phase Shift y=3sin(theta/4)-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 two hundred eighty-two million nine hundred fifty-five thousand eight hundred twenty-nine |
---|

- 1282955829 has 8 divisors, whose sum is
**1312767360** - The reverse of 1282955829 is
**9285592821** - Previous prime number is
**179**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 51
- Digital Root 6

Name | one billion four hundred ninety-nine million six hundred thirty-six thousand four hundred fifty-four |
---|

- 1499636454 has 8 divisors, whose sum is
**2999272920** - The reverse of 1499636454 is
**4546369941** - Previous prime number is
**3**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 51
- Digital Root 6

Name | one billion two hundred forty-two million one hundred seven thousand nine hundred eighty-four |
---|

- 1242107984 has 64 divisors, whose sum is
**6771878316** - The reverse of 1242107984 is
**4897012421** - Previous prime number is
**13**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 38
- Digital Root 2