# Find Amplitude, Period, and Phase Shift y=2sin((8pix)/3+(3pi)/2)

Find Amplitude, Period, and Phase Shift y=2sin((8pix)/3+(3pi)/2)
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 .
Cancel the common factor.
Rewrite the expression.
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 .
Move the leading negative in into the numerator.
Phase Shift:
Factor out of .
Phase Shift:
Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Multiply and .
Phase Shift:
Simplify the expression.
Multiply by .
Phase Shift:
Multiply by .
Phase Shift:
Move the negative in front of the fraction.
Phase Shift:
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the left)
Vertical Shift: None
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### Name

Name one billion seven hundred four million six hundred fifteen thousand six hundred eighteen

### Interesting facts

• 1704615618 has 8 divisors, whose sum is 3409231248
• The reverse of 1704615618 is 8165164071
• Previous prime number is 3

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 39
• Digital Root 3

### Name

Name one billion two hundred seventy million seven hundred fifty-seven thousand eight hundred ninety-seven

### Interesting facts

• 1270757897 has 4 divisors, whose sum is 1286843520
• The reverse of 1270757897 is 7987570721
• Previous prime number is 79

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 53
• Digital Root 8

### Name

Name one billion two hundred eighty-seven million two hundred sixty-two thousand five hundred thirty-five

### Interesting facts

• 1287262535 has 16 divisors, whose sum is 1665002304
• The reverse of 1287262535 is 5352627821
• Previous prime number is 1223

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 41
• Digital Root 5