# Find Amplitude, Period, and Phase Shift y=1/2cos((4pix)/5-pi/2)

Find Amplitude, Period, and Phase Shift y=1/2cos((4pix)/5-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 .
Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Multiply and .
Phase Shift:
Multiply by .
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 eight hundred twenty-five million three hundred sixty thousand three hundred twenty-six

### Interesting facts

• 825360326 has 16 divisors, whose sum is 1246687200
• The reverse of 825360326 is 623063528
• Previous prime number is 269

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 35
• Digital Root 8

### Name

Name one billion six hundred fifty-seven million nine hundred nine thousand seven hundred ninety-four

### Interesting facts

• 1657909794 has 8 divisors, whose sum is 2487134160
• The reverse of 1657909794 is 4979097561
• Previous prime number is 10443

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 57
• Digital Root 3

### Name

Name five hundred sixty-four million two hundred fifty-nine thousand six hundred fifty-five

### Interesting facts

• 564259655 has 8 divisors, whose sum is 678493584
• The reverse of 564259655 is 556952465
• Previous prime number is 491

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 47
• Digital Root 2