Graphing (1 Viewer)

[Monsterman]

When you graph y=cotx is there a value for Pi/2? because.. when i put it into a graphing calculator.. its continuous but since cot is 1/tanx doesnt the Pi/2 make it approach infinity to zero?

 

[jet]

It's zero - you have to take the limit.

 

[Monsterman]

It's zero - you have to take the limit.

thank you. just making sure

 

[Trebla]

It's zero - you have to take the limit.

Not quite, you have to look back at the DEFINITION of cot x.

Definition of tan x:
tan x = sin x / cos x

Definition of cot x:
cot x = cos x / sin x
(NOT 1 / tan x)

NB: cot x = 1 / tan x if and only if tan x is well defined.

 

[Monsterman]

Not quite, you have to look back at the DEFINITION of cot x.

Definition of tan x:
tan x = sin x / cos x

Definition of cot x:
cot x = cos x / sin x
(NOT 1 / tan x)

NB: cot x = 1 / tan x if and only if tan x is well defined.

what do you mean by "well defined"?

 

[theresekathryn]

what do you mean by "well defined"?

Princeton Dictionary
Well Defined: chiseled, having a clean and distinct outline as if precisely cut along the edges; "a finely chiseled nose"; "well-defined features"

 

[emmcyclopedia]

Just to clarify -
Trebla has just expressed [1/tanx] in a different form. It's still the same thing as [cosx/sinx].
By well defined, he's just pretty much saying that you have to express the equation in such a way that you can enter values and get defined answers.
i.e. you can't define [1/tan(pi/2)],
but u can find a definitive answer to [cos(pi/2)/sin(pi/2)]

=]

 

[Trebla]

Well defined means it gives something valid and definite (i.e. nothing undefined). Perhaps a more colourful term that some applied mathematicians like to use is "well behaved" lol

 

[Monsterman]

Thank you all.