Sin Cos And Tan

[Arcane Wizard]

I've always wondered what they actually do, does anybody happen to know?

[Darth Android]

sin( is the function of a sine wave, cos( "" cosine wave, tan( "" tangent wave (?) i think...

[Arcane Wizard]

Really? I had no idea.

Of course I know how to use them, but what do they really do with the number? I mean, what kind of calculations are behind sin/cos/tan?

[b__]

Ive never taken trig but i know what they do cause we use them all the time in physics. They are for figuring out different angle measures and sides of a triangle.

[Arcane Wizard]

I know what sin/cos/tan are and how to use them, I just want to know what they do exactly with the number you provide when using them.

When you say tan(20/10), for example, you get this nice number, but how does it calculate that number? What exact function can you replace sin/cos/tan with?

[sgm]

The trig functions are geometric (link).

[anduril66]

Does the TI use a formula to calculate sin, cos, and tan, or does it look it up in a table? What are cosh, sinh, and tanh?

[DarkerLine]

It might use taylor polynomials to approximate. Example:

sin(x) = x^9/9! - x^7/7! + x^5/5! - x^3/3! + x

cos(x) = x^8/8!- x^6/6! = x^4/4! - x^2/2! + 1

tan(x) = ? not sure ?

the sinh, cosh, tanh are easy.

sinh(x) = (e^x - 1) (e^x + 1)/(2e^x)

cosh(x) = e^x/2 + 1/(2e^x)

tanh(x) = sinh(x)/cosh(x)

[Jeremiah Walgren]

You'd probably want to take a trig related class if you want to have a good definition of what they can do. Basically, like stated before, they're used to figure the measurement of angle. Or, by using the arc of each function (arccos, arcsin, etc), you can figure out a missing side if you have one other side and an angle. Remember, there are certain conditions for each, so don't take this as law or anything. Just a quick summary.

sinh, cosh, tanh, etc, are the hyperbolic trig functions. I have no idea what these are used for.

[KD5YTX]

In a right triangle, in respect to the angle in question, the sine is the ratio of the opposite side over hypotenuse, cosine is the ratio of the adjancent side over the hypotenuse, and the tangent is the ratio of the opposite side over the adjacent side.


Reverence abounds over trigonemetric ratios.

[Jeremiah Walgren]

Although the functions work for any triangle.

[Arcane Wizard]

[CoBB]

Actually both sin and cos are special cases of the exponential function. Tan is just their ratio.

sin(x) = (exp(ix) - exp(-ix)) / (2i)
cos(x) = (exp(ix) + exp(-ix)) / 2
tan(x) = sin(x) / cos(x)

Hence, if you have the definition of the exponential function, you can derive all the trigs from it:

exp(x) = e^x = 1 + x + x^2 / 2! + x^3 / 3! + x^4 / 4! + ... (the more members the closer approximation; also if x is close to zero the approximation gets better)
e = lim(n -> inf) (1 + 1/n)^n

About degree/radian conversion:

1 deg = (pi / 180) rad
1 rad = (180 / pi) deg

E. g. sin(65 deg) = sin(65 * pi / 180) etc.

[DarkerLine]

[DarkerLine]

[CoBB]

That's the definition of sin and cos, I can't do anything about it. :)

You can find e^x using e. g. its Taylor series (it's in my post, have you really read it?). That formula remains valid for complex numbers (actually it's valid even if x is a matrix).

[DarkerLine]

I'm sure I will understand that by the end of the year, right now I can't.

[sgm]

[CoBB]

You need to change the minus to a plus as well.

[anduril66]

"You can find e^x using e. g. its Taylor series (it's in my post, have you really read it?). That formula remains valid for complex numbers (actually it's valid even if x is a matrix). "

No, but I would like to. I can't find it. How do you raise a number by i? (w/o usind e^i on a calculator). Reading http://staff.jccc.net/swilson/mathtopics/c...imagandtrig.htm , it seems you have to use cos (and sin).