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 two billion fifty-five million nine hundred fifty-three thousand eight hundred eighty-six

Interesting facts

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

Basic properties

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

Name

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

Interesting facts

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

Basic properties

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

Name

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

Interesting facts

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

Basic properties

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