Trigonometry Examples

cot (x)

$\cot (x)$

Step 1

For any

y = cot (x)

$y = \cot (x)$ , vertical asymptotes occur at

x = n π

$x = n π$ , where

n

$n$ is an integer. Use the basic period for

y = cot (x)

$y = \cot (x)$ ,

(0, π)

$(0, π)$ , to find the vertical asymptotes for

y = cot (x)

$y = \cot (x)$ . Set the inside of the cotangent function,

b x + c

$b x + c$ , for

y = a cot (b x + c) + d

$y = a \cot (b x + c) + d$ equal to

0

$0$ to find where the vertical asymptote occurs for

y = cot (x)

$y = \cot (x)$ .

x = 0

$x = 0$

Step 2

Set the inside of the cotangent function

x

$x$ equal to

π

$π$ .

x = π

$x = π$

Step 3

The basic period for

y = cot (x)

$y = \cot (x)$ will occur at

(0, π)

$(0, π)$ , where

0

$0$ and

π

$π$ are vertical asymptotes.

(0, π)

$(0, π)$

Step 4

Find the period

\frac{π}{| b |}

$\frac{π}{| b |}$ to find where the vertical asymptotes exist.

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Step 4.1

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

0

$0$ and

1

$1$ is

1

$1$ .

\frac{π}{1}

$\frac{π}{1}$

Step 4.2

Divide

π

$π$ by

1

$1$ .

π

$π$

π

$π$

Step 5

The vertical asymptotes for

y = cot (x)

$y = \cot (x)$ occur at

0

$0$ ,

π

$π$ , and every

π n

$π n$ , where

n

$n$ is an integer.

π n

$π n$

Step 6

There are only vertical asymptotes for tangent and cotangent functions.

Vertical Asymptotes:

x = π n

$x = π n$ for any integer

n

$n$

No Horizontal Asymptotes

No Oblique Asymptotes

Step 7