# Find Amplitude, Period, and Phase Shift y=2sin(4(x-1/2))+3

Find Amplitude, Period, and Phase Shift y=2sin(4(x-1/2))+3
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 and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
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 and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
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:
Cancel the common factor of and .
Factor out of .
Phase Shift:
Cancel the common factors.
Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
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 seven hundred eighty-six million nine hundred forty-four thousand nine hundred twenty-eight

### Interesting facts

• 786944928 has 512 divisors, whose sum is 7281135360
• The reverse of 786944928 is 829449687
• Previous prime number is 29

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 57
• Digital Root 3

### Name

Name two hundred twenty-three million five hundred seventy-nine thousand seven hundred twenty-five

### Interesting facts

• 223579725 has 16 divisors, whose sum is 429273216
• The reverse of 223579725 is 527975322
• Previous prime number is 3

### Basic properties

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

### Name

Name one hundred eighty-three million one hundred thirty thousand ninety-five

### Interesting facts

• 183130095 has 16 divisors, whose sum is 202524672
• The reverse of 183130095 is 590031381
• Previous prime number is 67

### Basic properties

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