Rewrite the expression as <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><mi>sin</mi><mrow><mo>(</mo><mfrac><mrow><mn>2</mn><mi>x</mi></mrow><mrow><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac><mo>)</mo></mrow><mo>+</mo><mn>4</mn></mstyle></math> .

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>

Find the period of <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><mi>sin</mi><mrow><mo>(</mo><mfrac><mrow><mn>2</mn><mi>x</mi></mrow><mrow><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</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>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> in the formula for period.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</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 factor.

Rewrite the expression.

Move <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Find the period of <math><mstyle displaystyle="true"><mn>4</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>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> in the formula for period.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</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 factor.

Rewrite the expression.

Move <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>π</mi></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><mo>-</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mrow><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mrow></mfrac></mstyle></math>

Cancel the common factor of <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> .

Cancel the common factor.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><menclose notation="updiagonalstrike"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac></menclose></mrow><mrow><menclose notation="updiagonalstrike"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac></menclose></mrow></mfrac></mstyle></math>

Divide <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

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

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mn>1</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>5</mn><mi>π</mi></mstyle></math>

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

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

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

- 751495428 has 64 divisors, whose sum is
**2585802240** - The reverse of 751495428 is
**824594157** - Previous prime number is
**31**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 45
- Digital Root 9

Name | forty-nine million nine hundred forty-eight thousand six hundred seventeen |
---|

- 49948617 has 8 divisors, whose sum is
**69493824** - The reverse of 49948617 is
**71684994** - Previous prime number is
**23**

- Is Prime? no
- Number parity odd
- Number length 8
- Sum of Digits 48
- Digital Root 3

Name | five hundred twenty-five million three hundred ten thousand seven hundred twenty |
---|

- 525310720 has 2048 divisors, whose sum is
**17624945520** - The reverse of 525310720 is
**027013525** - Previous prime number is
**11**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 25
- Digital Root 7