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>3</mn></mrow></mfrac><mo>)</mo></mrow><mo>+</mo><mn>1</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>3</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>3</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>3</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>1</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>3</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>3</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><mn>0</mn></mrow><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</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><mrow><mo>(</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></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>3</mn><mi>π</mi></mstyle></math>

Phase Shift: None

Vertical Shift: <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math>

Do you know how to Find Amplitude, Period, and Phase Shift y=1-3sin(2/3x)? 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 fourteen million one hundred fifty-three thousand one hundred fourteen |
---|

- 1214153114 has 4 divisors, whose sum is
**1821229674** - The reverse of 1214153114 is
**4113514121** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 23
- Digital Root 5

Name | one billion six hundred sixty million six hundred sixty-seven thousand five hundred sixty-five |
---|

- 1660667565 has 32 divisors, whose sum is
**2673709056** - The reverse of 1660667565 is
**5657660661** - Previous prime number is
**491**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 48
- Digital Root 3

Name | six hundred thirty-six million four hundred one thousand five hundred forty-one |
---|

- 636401541 has 8 divisors, whose sum is
**853940704** - The reverse of 636401541 is
**145104636** - Previous prime number is
**157**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 30
- Digital Root 3