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

Find Amplitude, Period, and Phase Shift y=1-3sin(2/3x)
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.
Move to the left of .
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.
Move to the left of .
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 one billion two hundred fourteen million one hundred fifty-three thousand one hundred fourteen

### Interesting facts

• 1214153114 has 4 divisors, whose sum is 1821229674
• The reverse of 1214153114 is 4113514121
• Previous prime number is 2

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 23
• Digital Root 5

### Name

Name one billion six hundred sixty million six hundred sixty-seven thousand five hundred sixty-five

### Interesting facts

• 1660667565 has 32 divisors, whose sum is 2673709056
• The reverse of 1660667565 is 5657660661
• Previous prime number is 491

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 48
• Digital Root 3

### Name

Name six hundred thirty-six million four hundred one thousand five hundred forty-one

### Interesting facts

• 636401541 has 8 divisors, whose sum is 853940704
• The reverse of 636401541 is 145104636
• Previous prime number is 157

### Basic properties

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