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

kylekatarn

2005-07-29 11:41:42

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

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

mewhoexactlywhat

2005-07-29 07:00:38

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.