Find Amplitude, Period, and Phase Shift y=2sin(x-1/2)+3

$y = 2 \sin (x - \frac{1}{2}) + 3$

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

$a = 2$

$b = 1$

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

$d = 3$

Find the amplitude $| a |$ .

Amplitude: $2$

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

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Find the period of $2 \sin (x - \frac{1}{2})$ .

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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 $3$ .

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

Divide $\frac{1}{2}$ by $1$ .

Phase Shift: $\frac{1}{2}$

List the properties of the trigonometric function.

Amplitude: $2$

Period: $2 π$

Phase Shift: $\frac{1}{2}$ ( $\frac{1}{2}$ to the right)

Vertical Shift: $3$

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Name

Name	two hundred twelve million two hundred thousand eight hundred thirty-eight

Interesting facts

212200838 has 4 divisors, whose sum is 318301260
The reverse of 212200838 is 838002212
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 26
Digital Root 8

Name

Name	two billion one hundred forty-five million eight hundred thirty-three thousand nine hundred ninety-eight

Interesting facts

2145833998 has 16 divisors, whose sum is 4012988544
The reverse of 2145833998 is 8993385412
Previous prime number is 11

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 52
Digital Root 7

Name

Name	five hundred thirty-seven million six hundred thirty-three thousand eight hundred eighteen

Interesting facts

537633818 has 4 divisors, whose sum is 806450730
The reverse of 537633818 is 818336735
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 44
Digital Root 8

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