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## #1 2005-07-29 07:00:38

mewhoexactlywhat
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### Relation between: inv, arc, co, arcco??

Can anyone tell me what the difference is, if any, between inverse _, arc_, co_, and _^-1, when refering  to any of the trigonometric ratios? Also, what would arcco_, and inverse co_ refer to? Thank you.

## #2 2005-07-29 11:41:42

kylekatarn
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### Re: Relation between: inv, arc, co, arcco??

lets clear things up a little.

Your have two types of trigonometric functions:Direct and Inverse
...sine (sin) and cosine(cos)  are the basic blocks for building all trigonometric functions
--------------------------
1)Direct trig. functions
------------------------
sin(x)
cos(x)

..now you can build others:
tan(x)=sin(x)/cos(x)
cosec(x)=1/sin(x)
sec(x)=1/cos(x)

Remember the following (it helps not messing up with secant and cosecant until you get used to them) :
[S]in -> [C]osec
[C]os -> [S]ec

--------------------------
2) Inverse trig. functions
--------------------------
direct.trig.func. <=> associated inverse func

sin(y)=x <=> y=arcsin(x)
cos(y)=x  <=> y=arccos(x)
tan(y)=x <=> y=arctan(x)
sec(y)=x <=> y=arcsec(x)
cosec(y)=x <=> y=arccosec(x)

An inverse function "undoes" what its associated function "does"

examples:
... if sin(A)=0.5 then A=arcsin(0.5)..
... arctan[tan(K)]=K
... arccosec(cosec(T)=0.1 <=> T=0.1

--------------------------
3) Inverse funcs and calculators
--------------------------
the functions you see in calculators: sin-¹( cos-¹( tan-¹( etc... are the inverse arc functions.

how to calculate arcsin(0.1)?
In your calc. *should* exist a key or menu with the 'command' SIN-¹(
just enter SIN-¹(0.1) and the result shows up on the display

Same applies to arccos: COS-¹( and arctan:TAN-¹(

->But most calculators don't have SEC/SEC-¹ and COSEC/COSEC-¹...(WHY TE*AS INSTRUME*S????? :@#\$#%"!!! > so you must use the other to build this ones...

btw..
If you want my personal opinion, I think its wrong naming those functions "something-¹()". If the notation ARC(...) was invented, why the hell calculator manufacturers decided to replace it by (func)-¹? ...It has some logic since the inverse of x is 1/x, or x-¹ .But the concept is a bit different as far as trigonometric functions are concerned so it would be more correct if calcs used the notation arcsin( arctan( arccos(...etc as all math students use.

p.s:I didn't mention hyperbolic trig. functions in order to give you a more "simple" answer. But if you'r curious I can explain them here also

Last edited by kylekatarn (2005-07-29 11:43:26)

## #3 2005-07-29 14:31:30

ganesh
Moderator

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### Re: Relation between: inv, arc, co, arcco??

That is neatly explained.
Both Sin-¹x and Arcsin x are one and the same, and both are in use in Mathematics Textbooks.
To make things simple, if Sin x = 1/2,
it follows that                  Sin -¹(1/2) = x
or                                 ArcSin(1/2)  = x

Character is who you are when no one is looking.