# Find Amplitude, Period, and Phase Shift y=2cos((8x)/3-2pi)

Find Amplitude, Period, and Phase Shift y=2cos((8x)/3-2pi)
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 .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
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:
Cancel the common factor of .
Factor out of .
Phase Shift:
Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Combine and .
Phase Shift:
Move to the left of .
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the right)
Vertical Shift: None
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### Name

Name two hundred fifty million three hundred fifty-four thousand eight hundred twenty-seven

### Interesting facts

• 250354827 has 8 divisors, whose sum is 370896080
• The reverse of 250354827 is 728453052
• Previous prime number is 9

### Basic properties

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

### Name

Name two billion one hundred forty-five million eight hundred ninety-four thousand three hundred fifty-eight

### Interesting facts

• 2145894358 has 16 divisors, whose sum is 3268520640
• The reverse of 2145894358 is 8534985412
• Previous prime number is 3739

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 49
• Digital Root 4

### Name

Name seven hundred twelve million five hundred eighty-four thousand eight hundred sixty-three

### Interesting facts

• 712584863 has 8 divisors, whose sum is 730663296
• The reverse of 712584863 is 368485217
• Previous prime number is 43

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 44
• Digital Root 8