# Find Amplitude, Period, and Phase Shift y=-4sin(x/3)-1

Find Amplitude, Period, and Phase Shift y=-4sin(x/3)-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.
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
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.
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:
Multiply by .
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: None
Vertical Shift:
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### Name

Name two hundred twenty-five million nine hundred seventy-nine thousand two hundred sixty

### Interesting facts

• 225979260 has 64 divisors, whose sum is 876107232
• The reverse of 225979260 is 062979522
• Previous prime number is 13

### Basic properties

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

### Name

Name one billion eight hundred sixty-three million three hundred seventy-six thousand six hundred fifty-four

### Interesting facts

• 1863376654 has 4 divisors, whose sum is 2795064984
• The reverse of 1863376654 is 4566733681
• Previous prime number is 2

### Basic properties

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

### Name

Name one billion seven hundred eighty-seven million four hundred fifty thousand two hundred eighty-three

### Interesting facts

• 1787450283 has 8 divisors, whose sum is 3177689408
• The reverse of 1787450283 is 3820547871
• Previous prime number is 3

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 45
• Digital Root 9