Use the form <math><mstyle displaystyle="true"><mi>a</mi><mi>cos</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>

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"><mo>-</mo><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"><mo>-</mo><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</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 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><mi>π</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></mfrac></mstyle></math>

Dividing two negative values results in a positive value.

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: None

Do you know how to Find Amplitude, Period, and Phase Shift y=-cos(-x+pi)? 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 | two hundred thirty-one million four hundred ten thousand seven hundred eighty-two |
---|

- 231410782 has 8 divisors, whose sum is
**347184936** - The reverse of 231410782 is
**287014132** - Previous prime number is
**7507**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 28
- Digital Root 1

Name | one billion five hundred seventy-six million six hundred thirty-eight thousand two hundred ninety-seven |
---|

- 1576638297 has 16 divisors, whose sum is
**1692979200** - The reverse of 1576638297 is
**7928366751** - Previous prime number is
**59**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 54
- Digital Root 9

Name | one billion nine hundred seventy-nine million one hundred sixty-seven thousand nine hundred sixty-two |
---|

- 1979167962 has 16 divisors, whose sum is
**4065318432** - The reverse of 1979167962 is
**2697619791** - Previous prime number is
**37**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 57
- Digital Root 3