Rewrite the expression as <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn><mi>sin</mi><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>-</mo><mn>9</mn><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><mn>2</mn><mi>x</mi><mo>-</mo><mn>9</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>2</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>2</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></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"><mn>2</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>2</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</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>9</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>9</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>

List the properties of the trigonometric function.

Amplitude: <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math>

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

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>9</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mn>9</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> to the right)

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

Do you know how to Find Amplitude, Period, and Phase Shift f(x)=1-3sin(2x-9)? 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 ninety-two million four hundred four thousand nine hundred ninety-two |
---|

- 1292404992 has 2048 divisors, whose sum is
**44235416736** - The reverse of 1292404992 is
**2994042921** - Previous prime number is
**947**

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

Name | one billion three hundred ninety-six million eight hundred sixty-five thousand eight hundred eighty-five |
---|

- 1396865885 has 8 divisors, whose sum is
**1691073720** - The reverse of 1396865885 is
**5885686931** - Previous prime number is
**113**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 59
- Digital Root 5

Name | seven hundred forty-two million three hundred eight thousand forty-three |
---|

- 742308043 has 4 divisors, whose sum is
**785973240** - The reverse of 742308043 is
**340803247** - Previous prime number is
**17**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 31
- Digital Root 4