Find Amplitude, Period, and Phase Shift y=csc(2x-pi)

$y = \csc (2 x - π)$

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

$a = 1$

$b = 2$

$c = π$

$d = 0$

Since the graph of the function $c s c$ does not have a maximum or minimum value, there can be no value for the amplitude.

Amplitude: None

Find the period of $\csc (2 x - π)$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $2$ 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: $\frac{π}{2}$

List the properties of the trigonometric function.

Amplitude: None

Period: $π$

Phase Shift: $\frac{π}{2}$ ( $\frac{π}{2}$ to the right)

Vertical Shift: None

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Name

Name	one billion four hundred sixty-two million four hundred ninety-four thousand seven hundred thirteen

Interesting facts

1462494713 has 4 divisors, whose sum is 1464558180
The reverse of 1462494713 is 3174942641
Previous prime number is 709

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 41
Digital Root 5

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Name	two hundred nineteen million two hundred twenty-two thousand one hundred sixteen

Interesting facts

219222116 has 16 divisors, whose sum is 494398080
The reverse of 219222116 is 611222912
Previous prime number is 127159

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 26
Digital Root 8

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Name	five hundred fifty-six million five hundred seventy-nine thousand five hundred seventy-nine

Interesting facts

556579579 has 16 divisors, whose sum is 574133184
The reverse of 556579579 is 975975655
Previous prime number is 71

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 58
Digital Root 4

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Convert Degrees, Minutes, Seconds to Decimal Degrees 41 degrees 36'40''