Find Amplitude, Period, and Phase Shift y=2cot(4x-pi)-2

$y = 2 \cot (4 x - π) - 2$

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

$a = 2$

$b = 4$

$c = π$

$d = - 2$

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

Amplitude: None

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

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Find the period of $2 \cot (4 x - π)$ .

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

$\frac{π}{| b |}$

Replace $b$ with $4$ in the formula for period.

$\frac{π}{| 4 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$\frac{π}{4}$

Find the period of $- 2$ .

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

$\frac{π}{| b |}$

Replace $b$ with $4$ in the formula for period.

$\frac{π}{| 4 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$\frac{π}{4}$

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

$\frac{π}{4}$

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: $\frac{π}{4}$

List the properties of the trigonometric function.

Amplitude: None

Period: $\frac{π}{4}$

Phase Shift: $\frac{π}{4}$ ( $\frac{π}{4}$ to the right)

Vertical Shift: $- 2$

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Name

Name	one billion two hundred thirty-three million five hundred forty-eight thousand eight hundred sixty-nine

Interesting facts

1233548869 has 16 divisors, whose sum is 1489100800
The reverse of 1233548869 is 9688453321
Previous prime number is 43

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 49
Digital Root 4

Name

Name	one billion six hundred eighty-three million six hundred twenty-seven thousand two hundred sixty-four

Interesting facts

1683627264 has 2048 divisors, whose sum is 52303242240
The reverse of 1683627264 is 4627263861
Previous prime number is 9

Basic properties

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

Name

Name	one billion three hundred eleven million two hundred forty-two thousand six hundred one

Interesting facts

1311242601 has 8 divisors, whose sum is 1758430080
The reverse of 1311242601 is 1062421131
Previous prime number is 173

Basic properties

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

Graph y=csc(x+(4pi)/5)

Graph f(x)=2 log base 5 of x+3-1

Convert to Interval Notation 11<=5x-4<=31

Graph -2-2tan(4x-2pi)

Find the Quadrant of the Angle -311