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

Find Amplitude, Period, and Phase Shift y=cos(6pix+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
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
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:
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:
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 seven hundred fifty-one million one hundred eighty-nine thousand five hundred twelve

### Interesting facts

• 1751189512 has 32 divisors, whose sum is 5922616320
• The reverse of 1751189512 is 2159811571
• Previous prime number is 479

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 40
• Digital Root 4

### Name

Name seven hundred sixty-three million eight hundred nineteen thousand one hundred fifty-five

### Interesting facts

• 763819155 has 64 divisors, whose sum is 1221350400
• The reverse of 763819155 is 551918367
• Previous prime number is 151

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 45
• Digital Root 9

### Name

Name two hundred ninety-four million one hundred twenty-five thousand nine hundred sixty-six

### Interesting facts

• 294125966 has 8 divisors, whose sum is 464409480
• The reverse of 294125966 is 669521492
• Previous prime number is 19

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 44
• Digital Root 8