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>4</mn></mstyle></math>

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

List the properties of the trigonometric function.

Amplitude: <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math>

Period: <math><mstyle displaystyle="true"><mn>8</mn><mi>π</mi></mstyle></math>

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

Vertical Shift: <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math>

Do you know how to Find Amplitude, Period, and Phase Shift y=4sin((x-pi)/4)-3? 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 eight hundred sixteen million one hundred three thousand four hundred four |
---|

- 1816103404 has 16 divisors, whose sum is
**4326599448** - The reverse of 1816103404 is
**4043016181** - Previous prime number is
**17**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 28
- Digital Root 1

Name | one billion four hundred fifty-five million four hundred thirteen thousand three hundred seventy-two |
---|

- 1455413372 has 32 divisors, whose sum is
**3871545120** - The reverse of 1455413372 is
**2733145541** - Previous prime number is
**29**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 35
- Digital Root 8

Name | two hundred seventy-four million seven hundred forty thousand eight hundred ninety-one |
---|

- 274740891 has 4 divisors, whose sum is
**366321192** - The reverse of 274740891 is
**198047472** - Previous prime number is
**3**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 42
- Digital Root 6