# Find Amplitude, Period, and Phase Shift y=3sin(2x+3pi)-1

Find Amplitude, Period, and Phase Shift y=3sin(2x+3pi)-1
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:
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:
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### Name

Name two billion one hundred eleven million six hundred sixty-six thousand two hundred nineteen

### Interesting facts

• 2111666219 has 8 divisors, whose sum is 2311383312
• The reverse of 2111666219 is 9126661112
• Previous prime number is 61

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 35
• Digital Root 8

### Name

Name eight hundred eighty-six million one hundred thirty-three thousand one hundred forty

### Interesting facts

• 886133140 has 32 divisors, whose sum is 2469740544
• The reverse of 886133140 is 041331688
• Previous prime number is 31

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 34
• Digital Root 7

### Name

Name six hundred forty-two million one hundred two thousand five hundred sixteen

### Interesting facts

• 642102516 has 16 divisors, whose sum is 1459324800
• The reverse of 642102516 is 615201246
• Previous prime number is 99

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 27
• Digital Root 9