# Find Amplitude, Period, and Phase Shift y=3cos((2x)/3+3pi)

Find Amplitude, Period, and Phase Shift y=3cos((2x)/3+3pi)
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
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move to the left of .
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:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Multiply .
Combine and .
Phase Shift:
Multiply by .
Phase Shift:
Combine and .
Phase Shift:
Phase Shift:
Move the negative in front of the fraction.
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the left)
Vertical Shift: None
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### Name

Name two hundred three million nine hundred thirty-nine thousand seven hundred fifty

### Interesting facts

• 203939750 has 32 divisors, whose sum is 453099744
• The reverse of 203939750 is 057939302
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 38
• Digital Root 2

### Name

Name one billion five hundred thirty-one million three hundred ninety-three thousand fifty-six

### Interesting facts

• 1531393056 has 512 divisors, whose sum is 16040566080
• The reverse of 1531393056 is 6503931351
• Previous prime number is 43

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 36
• Digital Root 9

### Name

Name four hundred twenty million two hundred thirty-nine thousand seventy-three

### Interesting facts

• 420239073 has 8 divisors, whose sum is 565759168
• The reverse of 420239073 is 370932024
• Previous prime number is 103

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 30
• Digital Root 3