# Find Amplitude, Period, and Phase Shift y=cos((6pix)/7+pi/2)

Find Amplitude, Period, and Phase Shift y=cos((6pix)/7+pi/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 nine hundred eighty-two million two hundred thirteen thousand seven hundred sixty-nine

### Interesting facts

• 1982213769 has 4 divisors, whose sum is 2642951696
• The reverse of 1982213769 is 9673122891
• Previous prime number is 3

### Basic properties

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

### Name

Name one billion five hundred ninety-three million six hundred thirty-two thousand four hundred twenty-eight

### Interesting facts

• 1593632428 has 32 divisors, whose sum is 3800251728
• The reverse of 1593632428 is 8242363951
• Previous prime number is 17

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 43
• Digital Root 7

### Name

Name two billion seventy-four million nine hundred forty-eight thousand four hundred thirty-nine

### Interesting facts

• 2074948439 has 8 divisors, whose sum is 2084040000
• The reverse of 2074948439 is 9348494702
• Previous prime number is 719

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 50
• Digital Root 5