Could someone explain to me, (in plain English if possible), what acos, asin and atan are and how they relate to geometry and cos, sin, and tan? Thanks.

acos, asin and atan are the inverse of cos, sin, and tan, that is, if y = acos x then x = cos y.

acos, asin and atan are the inverse functions of cos, sin and tan. This means that they "undo" anything done by the basic trig functions. For example, acos(cos(PI/4))==PI/4 and sin(asin(0.5))==0.5

They are usually used to find angles. For example, if you have a right-angled triangle with sides X, Y, and an hypotenuse H, then the angle between H and X is atan(Y/X) or asin(Y/H) or acos(X/H)

Good stuff,
Thanks again.

Just to add in something. You wanted to visualize it geometrically. I urge you to look at any graph be it trigonometric or algebraic. Lets say you're looking at a graph of a sine function which looks like a wave starting at (0,0) from the positive x axis and oscillating every 2 pi. rotate the graph 90 degrees clockwise and visually "flip" the graph as if to turn it in place around the vertical axis. That is an example of what asin (arcsine) or inverse sine would be. But also remember that a function can only have one y value for a given x value thus in real life the graph is restricted over an interval. sine, cosine tan etc are used to find a ratio of two sides for an angle that is calculated such as y = sin(45 deg). If you took that result and used the inverse function ,then 45 = asin(y). There are many tutorials out there on trigonometry that should help. Hopefully you should have a good grasp on lower level math like high school or college algebra first.


EDIT: looks like he already got it.

[edited by - nervo on July 24, 2003 6:58:04 AM]