# Find Amplitude, Period, and Phase Shift f(x)=-4-5cos(2x-pi)

Find Amplitude, Period, and Phase Shift f(x)=-4-5cos(2x-pi)
Rewrite the expression as .
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Find the amplitude .
Amplitude:
Find the period using the formula .
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Cancel the common factor of .
Cancel the common factor.
Divide by .
The period of addition/subtraction of trig functions is the maximum of the individual periods.
Find the phase shift using the formula .
The phase shift of the function can be calculated from .
Phase Shift:
Replace the values of and in the equation for phase shift.
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the right)
Vertical Shift:
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### Name

Name three million thirty-three thousand three hundred sixty-three

### Interesting facts

• 3033363 has 8 divisors, whose sum is 4096000
• The reverse of 3033363 is 3633303
• Previous prime number is 79

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 7
• Sum of Digits 21
• Digital Root 3

### Name

Name six hundred eighty-eight million six hundred seventy-six thousand five hundred sixty-three

### Interesting facts

• 688676563 has 8 divisors, whose sum is 716322816
• The reverse of 688676563 is 365676886
• Previous prime number is 31

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 55
• Digital Root 1

### Name

Name thirty-two million six hundred twenty-six thousand four hundred fifty-three

### Interesting facts

• 32626453 has 4 divisors, whose sum is 32656780
• The reverse of 32626453 is 35462623
• Previous prime number is 1117

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 8
• Sum of Digits 31
• Digital Root 4