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><mn>8</mn></mrow><mrow><mn>3</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"><mn>2</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> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Combine <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>π</mi></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><mn>2</mn><mi>π</mi></mrow><mrow><mfrac><mrow><mn>8</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></mfrac></mstyle></math>

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi><mrow><mo>(</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>8</mn></mrow></mfrac><mo>)</mo></mrow></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>2</mn><mi>π</mi></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mn>2</mn><mrow><mo>(</mo><mi>π</mi><mo>)</mo></mrow><mrow><mo>(</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>8</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math>

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mn>2</mn><mrow><mo>(</mo><mi>π</mi><mo>)</mo></mrow><mrow><mo>(</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mrow></mfrac><mo>)</mo></mrow></mstyle></math>

Cancel the common factor.

Phase Shift: <math><mstyle displaystyle="true"><menclose notation="updiagonalstrike"><mn>2</mn></menclose><mi>π</mi><mrow><mo>(</mo><mfrac><mrow><mn>3</mn></mrow><mrow><menclose notation="updiagonalstrike"><mn>2</mn></menclose><mo>⋅</mo><mn>4</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math>

Rewrite the expression.

Phase Shift: <math><mstyle displaystyle="true"><mi>π</mi><mrow><mo>(</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mi>π</mi><mrow><mo>(</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math>

Combine <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi><mo>⋅</mo><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>

Move <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>4</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"><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> to the right)

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=2cos((8x)/3-2pi)? 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 | two hundred fifty million three hundred fifty-four thousand eight hundred twenty-seven |
---|

- 250354827 has 8 divisors, whose sum is
**370896080** - The reverse of 250354827 is
**728453052** - Previous prime number is
**9**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 36
- Digital Root 9

Name | two billion one hundred forty-five million eight hundred ninety-four thousand three hundred fifty-eight |
---|

- 2145894358 has 16 divisors, whose sum is
**3268520640** - The reverse of 2145894358 is
**8534985412** - Previous prime number is
**3739**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 49
- Digital Root 4

Name | seven hundred twelve million five hundred eighty-four thousand eight hundred sixty-three |
---|

- 712584863 has 8 divisors, whose sum is
**730663296** - The reverse of 712584863 is
**368485217** - Previous prime number is
**43**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 44
- Digital Root 8