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Whats is tan?

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I never had trigonometry in school, and well to be honest I never studied math very well at all. However now that I do alot of 3D programming it sure would be nice to know it all, heh or at least some of it... Anyways to the question, what is tan? I thought tan gave you the hypotenuse of cos(a) and sin(a), but it doesnt. [edited by - pag on June 4, 2003 2:38:33 AM]

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quote:
Original post by pag
I never had trigonometry in school, and well to be honest I never studied math very well at all. However now that I do alot of 3D programming it sure would be nice to know it all, heh or at least some of it...

Anyways to the question, what is tan?
I thought tan gave you the hypotenuse of cos(a) and sin(a), but it doesnt.

[edited by - pag on June 4, 2003 2:38:33 AM]


sohcahtoa

s = sin
c = cos
t = tan
o = opposite
a = adjacent
h = hypotenuse

sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent

or

tan = (opposite / adjacent) (1) = (opposite / adjacent) (hypotenuse / hypotenuse) = (opposite / hypotenuse) (hypotenuse / adjacent) = sin / cos

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Make a right triangle, using a specific angle "a" for one of the non-90 angles. Tan(a) is the length of the side not touching (a) divided by the length of the side touching (a) and the 90 degree angle.

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tan(x)=sin(x)/cos(x)=

o/h o/h h o
---= --- * - = -
a/h a/h h a

where o is the opposite side to angle x and a is the adjacent side to x.


/|
h/ |
/ | o
/x |
----
a





doh, nuts. Mmmm... donuts
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[edited by - brassfish89 on June 4, 2003 2:21:22 PM]

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oke, thanks alot guys... However it would be nice with some examples of where this function is used. Like I know what cos and sin can be used for, but what about tan?

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Perspective projections. Imagine that you want to map a certain depth unit to a certain screen unit (for example, every 5 units farther from the viewer, the logical screen mapping increases by 1 unit or something). Over time, as the object moves farther away, the screen mapping will increase and increase, yet the physical screen is the same size, so the object appears to get smaller. This ratio can be described in terms of a FOV (field of view) angle, the tangeant of which describes the ratio of the screen mapping to the depth of an object.

Sorry if that was a confusing example, it was the first that came to my mind

[edited by - Zipster on June 4, 2003 6:36:29 PM]

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I find it easier to understand sine and cosine as (sin,cos) = (x,y) of the unit circle. That's pretty much how I learned it on my own (I learned it from a BASIC manual - but I'm not sure if it explained it this way, or if this is how I understood it ), and how I've used it since, and I've never had problems with it. I don't believe it's taught properly in school - no one really seems to understand by their method, and it creates more confusion than anything. Hope this helps...

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[edited by - Jason Doucette on June 4, 2003 9:39:28 PM]

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Well I dunno bout you, but my math teacher made us memorize important values on the unit circles and how they relate to angles using tan, sine, and cosine. Anyways, the points on the unit circle are made with the parametric function x=cos(t), y=sin(t) where t is the variable. Also, tan(t) would be the slope of the line from the origion to (x,y). Using just this info, we derived all the main trig identities, but I can''t remember offhand how we did it.

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Apparently, a "tan" is something you get when you got out into direct sunlight. I know, it sounds crazy, but apparently if you can survive out there for long enough, you''ll get slightly darker.

I wouldn''t advise many of the people here to try it, though. I imagine many of you risk getting a "burn", which is a bit like a "tan", but a whole lot more painful.

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The really interesting stuff is when you get into complex analysis, and look at the 4-dimensional graphs of trig functions. And inverse functions, and hyperbolic functions. The maclaurin series for those functions are all pretty cool too.

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