#### Archived

This topic is now archived and is closed to further replies.

# Whats is tan?

This topic is 5304 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

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]

##### Share on other sites
tan(x) = sin(x) / cos(x)

Too tired to explain it now though u_U

##### Share on other sites
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
h = hypotenuse

sin = opposite / hypotenuse

or

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

##### Share on other sites
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.

##### Share on other sites
atan(y)=\$[dx/(1+x^2)]

where:
y=tan(x) => x=atan(y) - atan() is opposite to tan()...

C++ RULEZ!!!

##### Share on other sites
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
My website

[edited by - brassfish89 on June 4, 2003 2:21:22 PM]

##### Share on other sites
I thought tan(x) was defined as the slope of the line tangent to sin(x).

##### Share on other sites
quote:
Original post by karmicthreat
I thought tan(x) was defined as the slope of the line tangent to sin(x).

The slope of the tangent line to sin(x) is cos(x).

##### Share on other sites
Your right, I don''t know what I was thinking. The derivative of sin is cos. But if you integrate tan you end up with -ln(|cos(X)|). So tan is just wack.

##### Share on other sites
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?

##### Share on other sites
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]

##### Share on other sites
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...

Jason Doucette - online resume page: www.jasondoucette.com
projects / games, real-time graphics, artificial intelligence, world records, wallpapers / desktops / backgrounds
"Great minds discuss ideas, average minds discuss events, small minds discuss people." - Anna Eleanor Roosevelt, 1884-1962

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

##### Share on other sites
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.

##### Share on other sites
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.

This useless post brought to you by the paint-sniffing pixies that are living inside my head.

The following statement is true. The previous statement is false.
Shameless promotion:
FreePop: The GPL Populous II clone.

##### Share on other sites
I think the intresting thing about using the trig functions is how you can use them to calculate angles in a coordinate system

coder requires 0xf00d before continue().

Killer Eagle Software

##### Share on other sites
what''s so interesting about that? It''s just ratios.

##### Share on other sites
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.

• ### Forum Statistics

• Total Topics
628710
• Total Posts
2984325

• 23
• 11
• 9
• 13
• 14