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

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

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

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

$b = 1$

$c = - \frac{π}{2}$

$d = 0$

Find the amplitude $| a |$ .

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

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

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

Period: $\frac{2 π}{| b |}$

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

Period: $\frac{2 π}{| 1 |}$

Solve the equation.

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

Period: $\frac{2 π}{1}$

Divide $2 π$ by $1$ .

Period: $2 π$

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: $\frac{- \frac{π}{2}}{1}$

Divide $- \frac{π}{2}$ by $1$ .

Phase Shift: $- \frac{π}{2}$

Find the vertical shift $d$ .

Vertical Shift: $0$

List the properties of the trigonometric function.

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

Period: $2 π$

Phase Shift: $- \frac{π}{2}$ ( $\frac{π}{2}$ to the left)

Vertical Shift: $0$

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Name

Name	six hundred ten million three hundred eighty-three thousand five hundred seventy-two

Interesting facts

610383572 has 16 divisors, whose sum is 1454149260
The reverse of 610383572 is 275383016
Previous prime number is 17

Basic properties

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

Name

Name	one billion five hundred fifty million four hundred sixty thousand one hundred three

Interesting facts

1550460103 has 4 divisors, whose sum is 1551138568
The reverse of 1550460103 is 3010640551
Previous prime number is 2293

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 25
Digital Root 7

Name

Name	one billion eight hundred eighty-six million one hundred forty-seven thousand three hundred eighty-five

Interesting facts

1886147385 has 64 divisors, whose sum is 3459456000
The reverse of 1886147385 is 5837416881
Previous prime number is 19

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 51
Digital Root 6

Solve Graphically sin(2x) = square root of 3cos(2x)

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Simplify sin(17)

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