Question

Question is inside!! :D

thanks :)

Answer 1

answer choices:

A. I only

B. II only

C. I and III only

D. I and IV only

**my answer; D. I and IV only

is that correct? :D

Answer 2

It would have asymptotes at those values if those values are not part of their domain.
So, which of these has no value, when
\[\Large x = n\pi\]?

Answer 3

Pro-tip.
Sine and Cosine have no asymptotes.

Answer 4

wait really?? so automatically sine and cosine will NEVER have asymptotes?

and what do u mean by the question? ;/

Answer 5

Well, sine and cosine are defined no matter what x is...
ie
sin(x)
and
cos(x)
always have values, for any real number x.

So... remember,
\[\tan x = \frac{\sin x}{\cos x}\]\[\cot x = \frac{\cos x}{\sin x}\]\[\sec x = \frac{1}{\cos x}\]\[\csc x = \frac1{\sin x}\]

Answer 6

So, each of these non-sine and non-cosine functions have denominators which COULD be zero, right?

Answer 7

i think so

Answer 8

So, between sin and cos, which one is zero, when x = n*pi?

Answer 9

can't neither of them be 0? because then it makes csc and sec undefined right? :/

Answer 10

Of course, it could be that neither of them are zero, but when is sine zero?
When is cosine zero?

In fact
\[\huge \sin \ n\pi=0 \ \ \ \ \ \ for \ all \ n\in\mathbb{Z}\]

Answer 11

ohhh okay so what does that mean?

Answer 12

So, if
\[\sin n\pi=0\]What does that mean for cot x and csc x?

Answer 13

Because cot x and csc x both have sin x in their denominators.

Answer 14

that they don't have asymptotes?

Answer 15

Means they DO have asymptotes :)

Answer 16

ohhhh i seee haha i got a bit confused for a sec.. lol

so the final answer is D. I and IV only?? because of the above? ^^

Answer 17

Okay, I'm going to preempt you...
The functions with asymptotes at \[\LARGE n\pi\]are the CO-functions, except cosine
Means they include cot and csc.

The functions with asymptotes at \[\LARGE \frac{\pi}{2}+n\pi\]are the non-CO-functions, except sine,
means they include tan and sec.

Answer 18

okay.. so i just need to try and memorize that right?? what u just wrote?

so is that right then? answer is D? :D csc and cot ?

Answer 19

That's right :)
No need to memorise, if you can help it, but it sure helps ^.^

Answer 20

hahah oaky!! :D

Answer 21

thanksss :D