# Find Amplitude, Period, and Phase Shift y=8cos(pi/4x-pi/2)

Find Amplitude, Period, and Phase Shift y=8cos(pi/4x-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.
Multiply by .
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 .
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Cancel the common factor of .
Factor out of .
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 right)
Vertical Shift: None
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### Name

Name one billion seven hundred eighteen million three hundred three thousand eight hundred thirty-two

### Interesting facts

• 1718303832 has 512 divisors, whose sum is 8465264640
• The reverse of 1718303832 is 2383038171
• Previous prime number is 47

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 36
• Digital Root 9

### Name

Name one billion six hundred eighty-three million three hundred forty-three thousand seven hundred ninety-six

### Interesting facts

• 1683343796 has 16 divisors, whose sum is 3788472924
• The reverse of 1683343796 is 6973433861
• Previous prime number is 4153

### Basic properties

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

### Name

Name one billion seven hundred eighty-six million nine hundred sixty thousand five hundred ninety-eight

### Interesting facts

• 1786960598 has 4 divisors, whose sum is 2680440900
• The reverse of 1786960598 is 8950696871
• Previous prime number is 2

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 59
• Digital Root 5