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

$y = \sin (3 x + 2 π)$

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

$a = 1$

$b = 3$

$c = - 2 π$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $1$

Find the period of $\sin (3 x + 2 π)$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $3$ in the formula for period.

$\frac{2 π}{| 3 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$\frac{2 π}{3}$

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: $\frac{- 2 π}{3}$

Move the negative in front of the fraction.

Phase Shift: $- \frac{2 π}{3}$

List the properties of the trigonometric function.

Amplitude: $1$

Period: $\frac{2 π}{3}$

Phase Shift: $- \frac{2 π}{3}$ ( $\frac{2 π}{3}$ to the left)

Vertical Shift: None

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Name

Name	one billion one hundred ninety million two hundred forty-nine thousand six hundred fifty-nine

Interesting facts

1190249659 has 4 divisors, whose sum is 1190322904
The reverse of 1190249659 is 9569420911
Previous prime number is 24337

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 46
Digital Root 1

Name

Name	one billion three hundred eighty-two million eighty-three thousand six hundred eighty-nine

Interesting facts

1382083689 has 8 divisors, whose sum is 1452559680
The reverse of 1382083689 is 9863802831
Previous prime number is 311

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 48
Digital Root 3

Name

Name	one billion eight hundred thirteen million four hundred two thousand two

Interesting facts

1813402002 has 32 divisors, whose sum is 3879755712
The reverse of 1813402002 is 2002043181
Previous prime number is 97

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 21
Digital Root 3

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