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>2</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> .

Period: <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"><mi>π</mi></mstyle></math> in the formula for period.

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

Solve the equation.

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

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

Cancel the common factor.

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

Divide <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

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

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

Period: <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><mfrac><mrow><mi>π</mi></mrow><mrow><mn>18</mn></mrow></mfrac></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math>

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>18</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math>

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

Cancel the common factor.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><menclose notation="updiagonalstrike"><mi>π</mi></menclose></mrow><mrow><mn>18</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</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><mn>1</mn></mrow><mrow><mn>18</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>18</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>18</mn></mrow></mfrac></mstyle></math>

Find the vertical shift <math><mstyle displaystyle="true"><mi>d</mi></mstyle></math> .

Vertical 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>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>

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

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>18</mn></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>18</mn></mrow></mfrac></mstyle></math> to the right)

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

Do you know how to Find Amplitude, Period, and Phase Shift y=-1/2*cos(pix-pi/18)? 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 | eight hundred eighty-one million one hundred three thousand nine hundred eighty-seven |
---|

- 881103987 has 32 divisors, whose sum is
**1326624768** - The reverse of 881103987 is
**789301188** - Previous prime number is
**23**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 45
- Digital Root 9

Name | one billion six hundred thirty-one million seventy-six thousand four hundred fifty-two |
---|

- 1631076452 has 16 divisors, whose sum is
**3692438352** - The reverse of 1631076452 is
**2546701361** - Previous prime number is
**163**

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

Name | one billion fifty million fifty-three thousand four hundred four |
---|

- 1050053404 has 16 divisors, whose sum is
**2383529328** - The reverse of 1050053404 is
**4043500501** - Previous prime number is
**113**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 22
- Digital Root 4