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>4</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>3</mn><mi>π</mi></mstyle></math> in the formula for period.

Cancel the common factor of <math><mstyle displaystyle="true"><mi>π</mi></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><mo>-</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mrow><mrow><mn>3</mn><mi>π</mi></mrow></mfrac></mstyle></math>

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn><mi>π</mi></mrow></mfrac></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn><mi>π</mi></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn><mi>π</mi></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn><mi>π</mi><mo>⋅</mo><mn>5</mn></mrow></mfrac></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>15</mn><mi>π</mi></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>15</mn><mi>π</mi></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>15</mn><mi>π</mi></mrow></mfrac></mstyle></math>

List the properties of the trigonometric function.

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

Period: <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>15</mn><mi>π</mi></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>15</mn><mi>π</mi></mrow></mfrac></mstyle></math> to the left)

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=4cos(3pix+2/5)? 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 | forty million seven hundred forty-one thousand seven hundred sixty-eight |
---|

- 40741768 has 16 divisors, whose sum is
**137503494** - The reverse of 40741768 is
**86714704** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 8
- Sum of Digits 37
- Digital Root 1

Name | four hundred thirty-eight million one hundred fifty-nine thousand two hundred seventy |
---|

- 438159270 has 16 divisors, whose sum is
**797168880** - The reverse of 438159270 is
**072951834** - Previous prime number is
**5**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 39
- Digital Root 3

Name | one billion four hundred forty-seven million six hundred forty-two thousand four hundred sixty-one |
---|

- 1447642461 has 8 divisors, whose sum is
**1932384384** - The reverse of 1447642461 is
**1642467441** - Previous prime number is
**881**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 39
- Digital Root 3