Find Amplitude, Period, and Phase Shift y=-4sin(x+3pi) ?

$y = - 4 \sin (x + 3 π)$ ?

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

$a = - 4$

$b = 1$

$c = - 3 π$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $4$

Find the period of $- 4 \sin (x + 3 π)$ .

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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 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: $\frac{- 3 π}{1}$

Divide $- 3 π$ by $1$ .

Phase Shift: $- 3 π$

List the properties of the trigonometric function.

Amplitude: $4$

Period: $2 π$

Phase Shift: $- 3 π$ ( $3 π$ to the left)

Vertical Shift: None

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Name

Name	one billion six hundred eighty-eight million nine hundred seventy-five thousand nine hundred eighty-nine

Interesting facts

1688975989 has 4 divisors, whose sum is 1696351660
The reverse of 1688975989 is 9895798861
Previous prime number is 229

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 70
Digital Root 7

Name

Name	two hundred eighty-three million one hundred seventy-five thousand five hundred forty-six

Interesting facts

283175546 has 16 divisors, whose sum is 440492040
The reverse of 283175546 is 645571382
Previous prime number is 421

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 41
Digital Root 5

Name

Name	three hundred five million two hundred twenty thousand three hundred fifty

Interesting facts

305220350 has 32 divisors, whose sum is 507506688
The reverse of 305220350 is 053022503
Previous prime number is 47

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 20
Digital Root 2

Factor f(x)=x^2+4x-32

Find the Exact Value csc(41)

Solve for ? cos(theta)+1=0

Graph m(x)=(19/4)^(-x)

Find the Exact Value (4sin(45)cos(45))/(tan(30)cot(30))