Chapter 6: Q. 6 (page 418)

True or False The graphs of
$y = \tan x, y = c o t x, y = s e c x, a n d y = c s c x$
each have infinitely many vertical asymptotes.

Short Answer

Expert verified

It is true that the graphs of $y = \tan x, y = c o t x, y = s e c x, a n d y = c s x$ each have infinitely many vertical asymptotes.

Step by step solution

Step 1. Given Information

The given functions are $y = \tan x, y = c o t x, y = s e c x, a n d y = c s x .$

We have to state whether it is true or false that each function have infinitely many vertical asymptotes.

Step 2. Finding whether the statement is true or false

The function $y = \tan x$ has asymptotes at $\pm \frac{n π}{2}$ . Hence it has infinite asymptotes.

The function $y = c o t x$ has asymptotes at $\pm n π .$ Hence it has infinite asymptotes.

The function $y = s e c x$ has asymptotes at $\pm \frac{n π}{2} .$ Hence it has infinite asymptotes.

The function $y = c s c x$ has asymptotes at $\pm n π .$ Hence it has infinite asymptotes.

Thus, the statement is true.

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True or False The graphs of
$y = \tan x, y = c o t x, y = s e c x, a n d y = c s c x$
each have infinitely many vertical asymptotes.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding whether the statement is true or false

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True or False The graphs of y=tanx,y=cotx,y=secx,andy=cscxeach have infinitely many vertical asymptotes.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding whether the statement is true or false

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True or False The graphs of
$y = \tan x, y = c o t x, y = s e c x, a n d y = c s c x$
each have infinitely many vertical asymptotes.