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

$y = \sin (2 (θ + π))$

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

$a = 1$

$b = 2$

$c = - 2 π$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $1$

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

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

$\frac{2 π}{| b |}$

Replace $b$ with $2$ in the formula for period.

$\frac{2 π}{| 2 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$\frac{2 π}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 π}{2}$

Divide $π$ by $1$ .

$π$

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: $\frac{- 2 π}{2}$

Cancel the common factor of $- 2$ and $2$ .

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Factor $2$ out of $- 2 π$ .

Phase Shift: $\frac{2 (- π)}{2}$

Cancel the common factors.

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Factor $2$ out of $2$ .

Phase Shift: $\frac{2 (- π)}{2 (1)}$

Cancel the common factor.

Phase Shift: $\frac{2 (- π)}{2 \cdot 1}$

Rewrite the expression.

Phase Shift: $\frac{- π}{1}$

Divide $- π$ by $1$ .

Phase Shift: $- π$

List the properties of the trigonometric function.

Amplitude: $1$

Period: $π$

Phase Shift: $- π$ ( $π$ to the left)

Vertical Shift: None

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Name

Name	one billion nine million two hundred sixty-nine thousand five hundred ninety-four

Interesting facts

1009269594 has 32 divisors, whose sum is 1702241280
The reverse of 1009269594 is 4959629001
Previous prime number is 163

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 45
Digital Root 9

Name

Name	five hundred seventy million twenty-two thousand sixty-nine

Interesting facts

570022069 has 4 divisors, whose sum is 579683520
The reverse of 570022069 is 960220075
Previous prime number is 59

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 31
Digital Root 4

Name

Name	eight hundred seventy-nine million two hundred fifty-four thousand sixteen

Interesting facts

879254016 has 4096 divisors, whose sum is 46625090400
The reverse of 879254016 is 610452978
Previous prime number is 29

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 42
Digital Root 6

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