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>4</mn></mrow><mrow><mn>5</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"><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><mn>0</mn></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"><mn>0</mn><mrow><mo>(</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mi>π</mi></mrow></mfrac><mo>)</mo></mrow></mstyle></math>

Multiply <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math>

List the properties of the trigonometric function.

Amplitude: <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math>

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

Phase Shift: None

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=4/5cos((pix)/2)? 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 one hundred ninety million one hundred sixty-three thousand one hundred ten |
---|

- 1190163110 has 16 divisors, whose sum is
**2145833856** - The reverse of 1190163110 is
**0113610911** - Previous prime number is
**607**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 23
- Digital Root 5

Name | one billion four hundred thirty-four million eight hundred fourteen thousand seven hundred fifty-six |
---|

- 1434814756 has 16 divisors, whose sum is
**3418235316** - The reverse of 1434814756 is
**6574184341** - Previous prime number is
**17**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 43
- Digital Root 7

Name | six hundred sixty-three million two hundred eighteen thousand six hundred ninety-six |
---|

- 663218696 has 128 divisors, whose sum is
**2596748544** - The reverse of 663218696 is
**696812366** - Previous prime number is
**337**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 47
- Digital Root 2