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"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></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>4</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>4</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</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 factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

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>2</mn><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</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> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mrow><mo>(</mo><mi>π</mi><mo>)</mo></mrow></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mn>2</mn><mo>⋅</mo><mn>2</mn></mrow></mfrac></mstyle></math>

Cancel the common factor.

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

Rewrite the expression.

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

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

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

List the properties of the trigonometric function.

Amplitude: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>

Period: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>

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

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=1/4cos(4x-2pi)? 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 four hundred seventeen million two hundred twenty-three thousand four hundred seventy-four |
---|

- 1417223474 has 16 divisors, whose sum is
**2166652800** - The reverse of 1417223474 is
**4743227141** - Previous prime number is
**199**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 35
- Digital Root 8

Name | one hundred sixty-eight million five hundred twenty-six thousand three hundred sixty-one |
---|

- 168526361 has 4 divisors, whose sum is
**171382800** - The reverse of 168526361 is
**163625861** - Previous prime number is
**59**

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

Name | one billion eight hundred thirty-eight million nine hundred fifty-two thousand nine hundred ninety-seven |
---|

- 1838952997 has 16 divisors, whose sum is
**2745026560** - The reverse of 1838952997 is
**7992598381** - Previous prime number is
**7**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 61
- Digital Root 7