Thread: sin and cosin

i didn't completely read all the posts in this thread, but:

you can use the law of sines and the law of cosines to find the missing sides if you get a side and an angle....

law of sines:
A/sin(a) = B/sin(b) = C/sin(c)

where segment A is oposite angle a, so on, so forth.

i can't quite remember the law of cosines....

thanks for all your advice guys...I'm going to try and desipher what you said...
i know that the cos and sin are ratios with the sides of the triangles, but so what if i know what the values are? What can i do once i get the value of sin and cosine?
thanks

>i know that the cos and sin are ratios with the sides of the
>triangles, but so what if i know what the values are? What can i
>do once i get the value of sin and cosine?

If you treat the cosine as being the function of a wave with representation

y = cos (t)

then you know what the amplitude of the wave will be at time t.

Perhaps a little too advanced, but to give an idea of what you can use sine and cosine also for: A periodic signal can be written as the sum of, when necessary infinite, sines and cosines.

Originally posted by ygfperson
the sine and cosine (and tangent, cotangent, cosecant, secant, and hyperbolic) functions are the sums of infinite numbers. their use is in relating a side of a triangle to its angle. it can also be used in circles and repeating waves because of their resemblance to triangles.

an example of an infinite series is pi (which is related to arctangent.)
PI/4 = 1/1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 ......

ygfperson, don't lead him to series in calc just yet.

Xterria, just play around with those functions in math.h using loops as an introduction.

Don't forget csc, cot and sec! We learned about these crazy things today.

Questions like, Prove:

sin(x) + 1 - cos(x)sec(x) = cos^3(x)
(Just an example, it probably won't work out)

A good way to investigate it would be through programming. For example try these test programs (susbstituting whatever your pixel drawing command is for putpixel.)

Code:

float t;
for (t = 0; t < 3.14 * 2; t += 0.01)
{
  putpixel(200 + cos(t),200 + sin(t));
}

Code:

float t;
for (t = 0; t < 3.14 * 2; t += 0.01)
{
  putpixel(100 * t, 200 + 100 * sin(t));
}

Code:

float t;
for (t = 0; t < 3.14 * 2; t += 0.01)
{
  printf("%f %f\n", t, sin(t)*sin(t) + cos(t)*cos(t));
}

Code:

float t;
for (t = 0; t < 3.14 * 2; t += 0.01)
{
  printf("%f %f %f\n", t, sin(t), cos(t + 3.14/2));
}