# Find Amplitude, Period, and Phase Shift f(t)=25sin(160pit)+115

Find Amplitude, Period, and Phase Shift f(t)=25sin(160pit)+115
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 .
The period of the function can be calculated using .
Period:
Replace with in the formula for period.
Period:
Solve the equation.
is approximately which is positive so remove the absolute value
Period:
Cancel the common factor of and .
Factor out of .
Period:
Cancel the common factors.
Factor out of .
Period:
Cancel the common factor.
Period:
Rewrite the expression.
Period:
Period:
Period:
Cancel the common factor of .
Cancel the common factor.
Period:
Rewrite the expression.
Period:
Period:
Period:
Period:
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:
Cancel the common factor of and .
Factor out of .
Phase Shift:
Cancel the common factors.
Factor out of .
Phase Shift:
Cancel the common factor.
Phase Shift:
Rewrite the expression.
Phase Shift:
Phase Shift:
Phase Shift:
Divide by .
Phase Shift:
Phase Shift:
Find the vertical shift .
Vertical Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the right)
Vertical Shift:
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### Name

Name one billion two hundred million three hundred thirty-three thousand forty

### Interesting facts

• 1200333040 has 64 divisors, whose sum is 7292023704
• The reverse of 1200333040 is 0403330021
• Previous prime number is 5

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 16
• Digital Root 7

### Name

Name one billion two hundred seventy-seven million one hundred thirty-nine thousand nine hundred fifty-five

### Interesting facts

• 1277139955 has 32 divisors, whose sum is 1591783424
• The reverse of 1277139955 is 5599317721
• Previous prime number is 223

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 49
• Digital Root 4

### Name

Name seven million seven hundred forty-two thousand six hundred twenty-four

### Interesting facts

• 7742624 has 128 divisors, whose sum is 59276448
• The reverse of 7742624 is 4262477
• Previous prime number is 131

### Basic properties

• Is Prime? no
• Number parity even
• Number length 7
• Sum of Digits 32
• Digital Root 5