Find Amplitude, Period, and Phase Shift y=2csc(x-pi)+1

$y = 2 \csc (x - π) + 1$

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

$a = 2$

$b = 1$

$c = π$

$d = 1$

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

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Find the period of $2 \csc (x - π)$ .

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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: None

Period: $2 π$

Phase Shift: $π$ ( $π$ to the right)

Vertical Shift: $1$

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Name

Name	two billion eighty-four million three hundred thousand three hundred thirty-nine

Interesting facts

2084300339 has 4 divisors, whose sum is 2273782200
The reverse of 2084300339 is 9330034802
Previous prime number is 11

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 32
Digital Root 5

Name

Name	one billion seven hundred five million eighty-nine thousand seven hundred sixty-one

Interesting facts

1705089761 has 4 divisors, whose sum is 1705790724
The reverse of 1705089761 is 1679805071
Previous prime number is 2441

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 44
Digital Root 8

Name

Name	nine hundred sixty-seven million three hundred fifty-two thousand seventy-two

Interesting facts

967352072 has 32 divisors, whose sum is 3377393820
The reverse of 967352072 is 270253769
Previous prime number is 29

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 41
Digital Root 5

Graph f(x)=x^2-3x-2

Factor f(x)=3x^3-16x^2-103x+36

Graph f(x)=8x^2+16x-7

Simplify cos(-(3 square root of 13)/13+1/2)

Simplify 6.8^2+10.5^2*2-2*6.8*(10.5cos(25.4))