Find Amplitude, Period, and Phase Shift y=4sin(x)

$y = 4 \sin (x)$

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

$a = 4$

$b = 1$

$c = 0$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $4$

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: $\frac{0}{1}$

Divide $0$ by $1$ .

Phase Shift: $0$

Find the vertical shift $d$ .

Vertical Shift: $0$

List the properties of the trigonometric function.

Amplitude: $4$

Period: $2 π$

Phase Shift: $0$ ( $0$ to the right)

Vertical Shift: $0$

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Name

Name	one hundred thirty million eight hundred eighty-four thousand seven hundred ninety-eight

Interesting facts

130884798 has 8 divisors, whose sum is 202276608
The reverse of 130884798 is 897488031
Previous prime number is 33

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 48
Digital Root 3

Name

Name	one billion seven hundred fifteen million three hundred fourteen thousand thirty-two

Interesting facts

1715314032 has 128 divisors, whose sum is 11668166640
The reverse of 1715314032 is 2304135171
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 27
Digital Root 9

Name

Name	two billion one hundred fourteen million five hundred five thousand one hundred thirteen

Interesting facts

2114505113 has 16 divisors, whose sum is 2442599040
The reverse of 2114505113 is 3115054112
Previous prime number is 293

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 23
Digital Root 5

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