# Find Amplitude, Period, and Phase Shift y=10sin((6pi)/4(x-pi/2))+25

Find Amplitude, Period, and Phase Shift y=10sin((6pi)/4(x-pi/2))+25
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.
Cancel the common factor of .
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
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.
Cancel the common factor of .
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
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:
Combine.
Phase Shift:
Cancel the common factor of .
Cancel the common factor.
Phase Shift:
Rewrite the expression.
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:
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:
Phase 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 thirty-five million nine hundred sixty-five thousand one hundred seventy-two

### Interesting facts

• 1235965172 has 32 divisors, whose sum is 3067888824
• The reverse of 1235965172 is 2715695321
• Previous prime number is 41

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 41
• Digital Root 5

### Name

Name one billion nine hundred four million five hundred seventy-seven thousand thirty-eight

### Interesting facts

• 1904577038 has 64 divisors, whose sum is 3576545280
• The reverse of 1904577038 is 8307754091
• Previous prime number is 383

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 44
• Digital Root 8

### Name

Name one billion nineteen million seven hundred eighty-six thousand six hundred eighty-one

### Interesting facts

• 1019786681 has 4 divisors, whose sum is 1019872500
• The reverse of 1019786681 is 1866879101
• Previous prime number is 14249

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 47
• Digital Root 2