# Find Amplitude, Period, and Phase Shift y=1/4cos(3pix)

Find Amplitude, Period, and Phase Shift y=1/4cos(3pix)
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 of .
The period of the function can be calculated using .
Replace with in the formula for period.
is approximately which is positive so remove the absolute value
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
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:
Cancel the common factor of and .
Factor out of .
Phase Shift:
Cancel the common factors.
Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Phase Shift:
Divide by .
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: None
Vertical Shift: None
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### Name

Name one billion seven hundred seventy-nine million one hundred thirty-two thousand three hundred sixty

### Interesting facts

• 1779132360 has 128 divisors, whose sum is 9811756800
• The reverse of 1779132360 is 0632319771
• Previous prime number is 47

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 39
• Digital Root 3

### Name

Name seven hundred twenty-nine million nine hundred forty-nine thousand six hundred eighteen

### Interesting facts

• 729949618 has 4 divisors, whose sum is 1094924430
• The reverse of 729949618 is 816949927
• Previous prime number is 2

### Basic properties

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

### Name

Name two billion one hundred fifteen million seven hundred forty-nine thousand five hundred

### Interesting facts

• 2115749500 has 64 divisors, whose sum is 5947512480
• The reverse of 2115749500 is 0059475112
• Previous prime number is 1259

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 34
• Digital Root 7