# Find Amplitude, Period, and Phase Shift f(x)=-1/2cos(4(x+pi/4))+1

Find Amplitude, Period, and Phase Shift f(x)=-1/2cos(4(x+pi/4))+1
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 using the formula .
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
The period of addition/subtraction of trig functions is the maximum of the individual periods.
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:
Move the negative in front of the fraction.
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the left)
Vertical Shift:
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### Name

Name one billion seven hundred forty-seven million six hundred sixty-five thousand three hundred twenty-one

### Interesting facts

• 1747665321 has 8 divisors, whose sum is 2356403040
• The reverse of 1747665321 is 1235667471
• Previous prime number is 89

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 42
• Digital Root 6

### Name

Name two hundred eighty-three million nine hundred sixty-six thousand nine hundred twenty-seven

### Interesting facts

• 283966927 has 8 divisors, whose sum is 294184800
• The reverse of 283966927 is 729669382
• Previous prime number is 727

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 52
• Digital Root 7

### Name

Name three hundred thirty-five million three hundred twenty-five thousand two hundred forty

### Interesting facts

• 335325240 has 128 divisors, whose sum is 1522501920
• The reverse of 335325240 is 042523533
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 27
• Digital Root 9