# Find Amplitude, Period, and Phase Shift y=cos((2pix)/3+1/3)

Find Amplitude, Period, and Phase Shift y=cos((2pix)/3+1/3)
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 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 .
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:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
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 nine hundred thirty-eight million six hundred two thousand five hundred seventy

### Interesting facts

• 938602570 has 8 divisors, whose sum is 1689484644
• The reverse of 938602570 is 075206839
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 40
• Digital Root 4

### Name

Name one billion five hundred twelve million thirty-two thousand eight hundred seventy

### Interesting facts

• 1512032870 has 8 divisors, whose sum is 2294732496
• The reverse of 1512032870 is 0782302151
• Previous prime number is 85

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 29
• Digital Root 2

### Name

Name seven hundred fifty-nine million one hundred ninety-six thousand two hundred seven

### Interesting facts

• 759196207 has 8 divisors, whose sum is 946530432
• The reverse of 759196207 is 702691957
• Previous prime number is 11

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 46
• Digital Root 1