# Find Amplitude, Period, and Phase Shift y=2cos(1/2x)+1

Find Amplitude, Period, and Phase Shift y=2cos(1/2x)+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.
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
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.
Multiply by .
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:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Multiply by .
Phase Shift:
Phase Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: None
Vertical Shift:
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### Name

Name one billion seven hundred sixty-three million fifty-nine thousand one hundred two

### Interesting facts

• 1763059102 has 64 divisors, whose sum is 3620275200
• The reverse of 1763059102 is 2019503671
• Previous prime number is 7

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 34
• Digital Root 7

### Name

Name one hundred ninety-two million three hundred seventy-eight thousand one hundred sixty-four

### Interesting facts

• 192378164 has 32 divisors, whose sum is 492734016
• The reverse of 192378164 is 461873291
• Previous prime number is 23

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 41
• Digital Root 5

### Name

Name six hundred seventy-five million seven hundred sixty-five thousand one hundred eighty-nine

### Interesting facts

• 675765189 has 16 divisors, whose sum is 1310575104
• The reverse of 675765189 is 981567576
• Previous prime number is 11

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 54
• Digital Root 9