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>2</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><mi>π</mi></mrow><mrow><mn>2</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"><mi>π</mi></mstyle></math> .

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

Cancel the common factor.

Rewrite the expression.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</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><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mrow><mrow><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mfrac></mstyle></math>

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math>

Cancel the common factor of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Move the leading negative in <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> into the numerator.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math>

Factor <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mi>π</mi></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi><mo>⋅</mo><mo>-</mo><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math>

Cancel the common factor.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><menclose notation="updiagonalstrike"><mi>π</mi></menclose><mo>⋅</mo><mo>-</mo><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>2</mn></mrow><mrow><menclose notation="updiagonalstrike"><mi>π</mi></menclose></mrow></mfrac></mstyle></math>

Rewrite the expression.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>⋅</mo><mn>2</mn></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>⋅</mo><mn>2</mn></mstyle></math>

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>6</mn></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mrow><mn>2</mn><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></mfrac><mo>⋅</mo><mn>2</mn></mstyle></math>

Cancel the common factor.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mrow><menclose notation="updiagonalstrike"><mn>2</mn></menclose><mo>⋅</mo><mn>3</mn></mrow></mfrac><mo>⋅</mo><menclose notation="updiagonalstrike"><mn>2</mn></menclose></mstyle></math>

Rewrite the expression.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math>

Move the negative in front of the fraction.

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math>

List the properties of the trigonometric function.

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

Period: <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> to the left)

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=2cos(pi/2x+pi/6)? 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 | nine hundred thirty-three million eight hundred seventy thousand nine hundred sixty-seven |
---|

- 933870967 has 4 divisors, whose sum is
**933988896** - The reverse of 933870967 is
**769078339** - Previous prime number is
**109391**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 52
- Digital Root 7

Name | thirty-five million sixty-nine thousand one hundred fifty-six |
---|

- 35069156 has 8 divisors, whose sum is
**78905610** - The reverse of 35069156 is
**65196053** - Previous prime number is
**2**

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

Name | five hundred seventy-nine million five hundred seventy-one thousand four hundred |
---|

- 579571400 has 64 divisors, whose sum is
**2036824920** - The reverse of 579571400 is
**004175975** - Previous prime number is
**1213**

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