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><mn>3</mn><mi>x</mi><mo>-</mo><mn>6</mn><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"><mn>3</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>3</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Find the period of <math><mstyle displaystyle="true"><mn>5</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>3</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>3</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>3</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>6</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math>

Divide <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

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

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

List the properties of the trigonometric function.

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

Period: <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> (<math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the right)

Vertical Shift: <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math>

Do you know how to Find Amplitude, Period, and Phase Shift y=4sin(3(x-2))+5? 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 six hundred four million one hundred ninety-seven thousand two hundred fifty-seven |
---|

- 1604197257 has 4 divisors, whose sum is
**1645330560** - The reverse of 1604197257 is
**7527914061** - Previous prime number is
**39**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 42
- Digital Root 6

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

- 438765053 has 8 divisors, whose sum is
**465418872** - The reverse of 438765053 is
**350567834** - Previous prime number is
**557**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 41
- Digital Root 5

Name | one billion nine hundred three million thirty-six thousand seven hundred thirty-two |
---|

- 1903036732 has 32 divisors, whose sum is
**4517679600** - The reverse of 1903036732 is
**2376303091** - Previous prime number is
**433**

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