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>1</mn></mstyle></math>

Find the period of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>π</mi><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>1</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>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

Find the period of <math><mstyle displaystyle="true"><mo>-</mo><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>1</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>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

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

Period: <math><mstyle displaystyle="true"><mn>2</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>1</mn></mstyle></math>

Do you know how to Find Amplitude, Period, and Phase Shift y=sin(x-pi)-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 | three hundred eighteen million one hundred ninety thousand one hundred sixty-nine |
---|

- 318190169 has 32 divisors, whose sum is
**383324160** - The reverse of 318190169 is
**961091813** - Previous prime number is
**67**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 38
- Digital Root 2

Name | sixty-eight million eight hundred seventy-three thousand two hundred forty |
---|

- 68873240 has 32 divisors, whose sum is
**278936784** - The reverse of 68873240 is
**04237886** - Previous prime number is
**5**

- Is Prime? no
- Number parity even
- Number length 8
- Sum of Digits 38
- Digital Root 2

Name | one billion eight hundred eighty-nine million six hundred thirty thousand nine hundred one |
---|

- 1889630901 has 4 divisors, whose sum is
**2099589900** - The reverse of 1889630901 is
**1090369881** - Previous prime number is
**9**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 45
- Digital Root 9