# Find Amplitude, Period, and Phase Shift y=4+3sin(pi/3x-pi/16)

Find Amplitude, Period, and Phase Shift y=4+3sin(pi/3x-pi/16)
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.
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.
Multiply by .
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.
Multiply 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:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Cancel the common factor of .
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Combine and .
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 one billion eight hundred sixty-eight million seven hundred five thousand eight hundred eighty-seven

### Interesting facts

• 1868705887 has 4 divisors, whose sum is 1886170536
• The reverse of 1868705887 is 7885078681
• Previous prime number is 107

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 58
• Digital Root 4

### Name

Name two billion forty million two hundred eighteen thousand forty-eight

### Interesting facts

• 2040218048 has 512 divisors, whose sum is 25481174400
• The reverse of 2040218048 is 8408120402
• Previous prime number is 199

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 29
• Digital Root 2

### Name

Name one hundred sixty-one million six hundred ninety-two thousand eight hundred seventy-two

### Interesting facts

• 161692872 has 128 divisors, whose sum is 798050880
• The reverse of 161692872 is 278296161
• Previous prime number is 197

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 42
• Digital Root 6