Find Amplitude, Period, and Phase Shift y=sin(x-pi)-1

$y = \sin (x - π) - 1$

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

$a = 1$

$b = 1$

$c = π$

$d = - 1$

Find the amplitude $| a |$ .

Amplitude: $1$

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

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Find the period of $\sin (x - π)$ .

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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 period of $- 1$ .

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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 $1$ .

$2 π$

The period of addition/subtraction of trig functions is the maximum of the individual periods.

$2 π$

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: $\frac{π}{1}$

Divide $π$ by $1$ .

Phase Shift: $π$

List the properties of the trigonometric function.

Amplitude: $1$

Period: $2 π$

Phase Shift: $π$ ( $π$ to the right)

Vertical Shift: $- 1$

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Name

Name	one billion seven hundred twenty-one million nine hundred forty-four thousand eight hundred thirty-four

Interesting facts

1721944834 has 4 divisors, whose sum is 2582917254
The reverse of 1721944834 is 4384491271
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 43
Digital Root 7

Name

Name	one billion eight hundred eight million four hundred sixty-three thousand five hundred fifty-six

Interesting facts

1808463556 has 64 divisors, whose sum is 4271097600
The reverse of 1808463556 is 6553648081
Previous prime number is 43

Basic properties

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

Name

Name	five hundred twenty-nine million seven hundred twenty thousand six hundred six

Interesting facts

529720606 has 4 divisors, whose sum is 794580912
The reverse of 529720606 is 606027925
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 37
Digital Root 1

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