Find Amplitude, Period, and Phase Shift y=1/2sin(x-pi)+1

$y = \frac{1}{2} \sin (x - π) + 1$

Use the form $a \sin (b x - c) + d$ to find the variables used to find the amplitude, period, phase shift, and vertical shift.

$a = \frac{1}{2}$

$b = 1$

$c = π$

$d = 1$

Find the amplitude $| a |$ .

Amplitude: $\frac{1}{2}$

Find the period using the formula $\frac{2 π}{| b |}$ .

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Find the period of $\frac{\sin (x - π)}{2}$ .

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The period of the function can be calculated using $\frac{2 π}{| b |}$ .

$\frac{2 π}{| b |}$

Replace $b$ with $1$ in the formula for period.

$\frac{2 π}{| 1 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{2 π}{1}$

Divide $2 π$ by $1$ .

$2 π$

Find the period of $1$ .

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The period of the function can be calculated using $\frac{2 π}{| b |}$ .

$\frac{2 π}{| b |}$

Replace $b$ with $1$ in the formula for period.

$\frac{2 π}{| 1 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{2 π}{1}$

Divide $2 π$ by $1$ .

$2 π$

The period of addition/subtraction of trig functions is the maximum of the individual periods.

$2 π$

Find the phase shift using the formula $\frac{c}{b}$ .

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The phase shift of the function can be calculated from $\frac{c}{b}$ .

Phase Shift: $\frac{c}{b}$

Replace the values of $c$ and $b$ in the equation for phase shift.

Phase Shift: $\frac{π}{1}$

Divide $π$ by $1$ .

Phase Shift: $π$

List the properties of the trigonometric function.

Amplitude: $\frac{1}{2}$

Period: $2 π$

Phase Shift: $π$ ( $π$ to the right)

Vertical Shift: $1$

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Name

Name	five hundred thirteen million eight hundred nine thousand one hundred eighty

Interesting facts

513809180 has 16 divisors, whose sum is 1387284840
The reverse of 513809180 is 081908315
Previous prime number is 5

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 35
Digital Root 8

Name

Name	two billion one hundred two million nine hundred twenty-eight thousand seven hundred twenty-eight

Interesting facts

2102928728 has 32 divisors, whose sum is 7098273000
The reverse of 2102928728 is 8278292012
Previous prime number is 13649

Basic properties

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

Name

Name	one billion seven hundred seventy-nine million three hundred seventeen thousand nine hundred thirty-three

Interesting facts

1779317933 has 4 divisors, whose sum is 1780766940
The reverse of 1779317933 is 3397139771
Previous prime number is 1229

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 50
Digital Root 5

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