# Find Amplitude, Period, and Phase Shift y=cos((6pix)/5+pi/3)

Find Amplitude, Period, and Phase Shift y=cos((6pix)/5+pi/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 .
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 three hundred thirty-eight million nine hundred sixty-six thousand six hundred twenty-eight

### Interesting facts

• 338966628 has 64 divisors, whose sum is 938710080
• The reverse of 338966628 is 826669833
• Previous prime number is 13

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 51
• Digital Root 6

### Name

Name one billion six hundred thirty-seven million six hundred eighty thousand six hundred forty-six

### Interesting facts

• 1637680646 has 32 divisors, whose sum is 3210170880
• The reverse of 1637680646 is 6460867361
• Previous prime number is 5659

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 47
• Digital Root 2

### Name

Name one billion seven hundred eighty-three million one hundred ninety-one thousand one hundred sixty-two

### Interesting facts

• 1783191162 has 16 divisors, whose sum is 3624848352
• The reverse of 1783191162 is 2611913871
• Previous prime number is 61

### Basic properties

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