Rewrite the expression as <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn><mi>cos</mi><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>-</mo><mi>π</mi><mo>)</mo></mrow><mo>-</mo><mn>4</mn></mstyle></math> .

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>5</mn></mstyle></math>

Find the period of <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn><mi>cos</mi><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>-</mo><mi>π</mi><mo>)</mo></mrow></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>2</mn></mstyle></math> in the formula for period.

The absolute value is the distance between a number and zero. The distance between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

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

Find the period of <math><mstyle displaystyle="true"><mo>-</mo><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>2</mn></mstyle></math> in the formula for period.

The absolute value is the distance between a number and zero. The distance between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

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

The period of addition/subtraction of trig functions is the maximum of the individual periods.

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><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>

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

List the properties of the trigonometric function.

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

Period: <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math>

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

Vertical Shift: <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math>

Do you know how to Find Amplitude, Period, and Phase Shift f(x)=-4-5cos(2x-pi)? 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 billion fifty-five million nine hundred fifty-three thousand eight hundred eighty-six |
---|

- 2055953886 has 16 divisors, whose sum is
**4699323264** - The reverse of 2055953886 is
**6883595502** - Previous prime number is
**7**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 51
- Digital Root 6

Name | two billion sixty-one million four hundred ninety-one thousand three hundred thirty-three |
---|

- 2061491333 has 8 divisors, whose sum is
**2277367680** - The reverse of 2061491333 is
**3331941602** - Previous prime number is
**79**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 32
- Digital Root 5

Name | four hundred seventy-three million three hundred ninety-two thousand five hundred four |
---|

- 473392504 has 64 divisors, whose sum is
**1644390720** - The reverse of 473392504 is
**405293374** - Previous prime number is
**37**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 37
- Digital Root 1