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

Too tired to explain it now though u_U

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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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+ "some advanced stuff" :
atan(y)=\$[dx/(1+x^2)]

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

C++ RULEZ!!!

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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
My website

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

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I thought tan(x) was defined as the slope of the line tangent to sin(x).

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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).

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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.

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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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