View Full Version : sin and cosin

Xterria

05-24-2002, 07:46 PM

ok, this may sound really rediculous but i want to know what sin and cosine are. I know they have somthing to do with triangles. Could any of you tell me what they are? My math book won't, and i searched on google and it just gave me 'expansions' on sin and cosine.

I really wanna learn so I can be ahead of my class(7th grade)

thanks!

Commander

05-24-2002, 07:59 PM

you could use them to find the missing sides or angles of a right triangle....

you could also find sides and angles for other triangles too, but then you have to use something called the sine or the cosine law

Xterria

05-24-2002, 08:03 PM

but can't you use the Pythorgiam(sp?) theory for that?

ya know

C^2 = A^2 + B^2?

Commander

05-24-2002, 08:04 PM

yes, but if they give you one side and one angle and ask you to solve the triangle, you can't use pythagoriam(??) theoram(??) since it dosen't deal with angles, but sine and cosine does

*sob*

I didn't know in grade 7 either. I wanted to, but I couldn't really find the info. it was just generally - yeah, you use those functions to do neato 3d thingiemabobbers.

not too complex. they are ratios on a right angle triangle

|\

| \

| \ y

x| \

|____\

z

the tangent is the length of the side x divided by the length of side z. the cosine is side y over side z, and the sine is side y over side x. forgive me if I've scrambled that a bit, somebody who has his head screwed on right will get it ok ;)

anyway, each value of sin(x), and cos(x), and tan(x), refers to the ratio of the length of each side over the other sides for angle x between either sides x and y or z and y, but not side x and z. there's a difference, but I'm messing it up.

you can use these ratios to do neat things like determine the angle between two vectors without a protractor or similar tool (if there were even equivalents in computer land) or rotate points about an axis.

my suggestion for the first use of these functions is to write a program that draws the graph of each function. - eg

for(x = 0; x < 320; x++)

plotmeabloodypixel(x, (sin(x) * 25)+75);

for screen mode 320 x 200 x 256 - change numbers for different screen modes. you'll see the function has a curve - which is handy without going into the meaning of the actual functions.

you can do things like draw wavy text, or flags, with the functions without trying to understand why it should work. good fun. um, i'm rambling. i'll post before-

ygfperson

05-24-2002, 08:11 PM

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 ......

golfinguy4

05-24-2002, 08:14 PM

XTERRIA, Noooooooooooooooooooo

Another corrupted mind. Wait till Pre-Calc. You will do so much of this crap u won't want to see them or hear of them again. Trust me. I have graphed so many of these and with transformations.:( All by hand as well.:mad: :( :( :mad:

Xterria

05-24-2002, 08:17 PM

so say I have (may i steal the triangle?)

|\

| \

| \ y = 20

x=?| \

|___\

z = 10

how would I use sin/cosine to find x?

thanks

Dual-Catfish

05-24-2002, 08:24 PM

SOH CAH TOA

Sine - Opposite, Hypotinuse

Cosine - Adjacent, Hypotenuse

Tangent - Opposite, Adjacent

You're also going to need Algebra 1 if you're going to do any of this. These functions also allow you to find angles inside the triangle.

Commander

05-24-2002, 08:25 PM

in this case, u don't need cosine becuse there in no angles involved, you could just use pyth ther to solve it!

Commander

05-24-2002, 08:30 PM

Lemme give u an example with a different triangle

(Theta is a Greek letter that look like a 0 with a horizontal line through it)

sin theta = opposite/hypotenuse

cos theta = adjacent/hypotenuse

c

|\

|_\

|40\ 12

| \

| \

|_____\

a b

if angle acb = theta

then

sin 40 = ab/12

cos 40 = ca/12

see now you can solve the equations and find the two other missing side and the angle!

You couldn’t do this with pyth therm

Shiro

05-25-2002, 04:40 AM

The sine and cosine are functions. When plotting the graphs of these functions, you get periodic waves of infinite length. Sine and cosine have many applications, not only in geometry. There are many formula's in geometry which allow you to calculate stuff. But since sine and cosine are both waves, they also appear in wave analysis, they are also very useful when playing with differential equations etc.

See also an explanation in this wonderful math reference:

http://mathworld.wolfram.com/Cosine.html

Xterria

05-25-2002, 12:26 PM

holy crackers i dont even know half the symbol in that site

Unregistered

05-25-2002, 12:55 PM

Originally posted by Xterria

holy crackers i dont even know half the symbol in that site

i wouldnt expect so lol you dont even get sin & cos so how can you even think to understand calculus?

dbaryl

05-25-2002, 01:33 PM

Xterria, I'm going to keep this nice and simple (and it is). If you take a look at a right triangle (attached), you will see that if I was to enlarge it by a factor of 2, each side will double, right? This means that the ratio of any two sides would stay the same, no matter what the scale was.

This is fact is used to help us find missing sides or angles of a triangle. For example, for an angle of 45°, no matter how big I make the sides, the ratio of adjacent side to hypotenuse is always 1 / (sqrt 2). Each angle has it's own ratio, and these the calculator remembers as either sine, cosine or tangent.

So, if I was to tell you that the base of a right triangle is 4 and the height is 3, what is the base angle? You know that the side opposite this angle is 3, and the adjacent side is 4. So, tangent (opposite / adjacent) of this angle is 3/4 or 0.75. Well, we now know that the tanglent of the missing angle is 3/4, but how do we get to the angle? One way is to take the calculator, and start taking the tangent of random angle until you get to about 0.75.

This could take a while, so you you think there is a way to do it differently... and there is. If we already know the tangent of an angle, there must be a way to 'extract' the angle from it, don't you think? Well, the inverse functions do just that. Inverse tangent (or tan-1) allows you to find the angle for whith the tangent is know. So, we use that calculator, punch is tan-1 (0.75) and there it is! Approx. 37°.

The ratios to keep in mind are

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

tan = opposite/adjacent

An esier way to remember this is this: SOH - CAH - TOA

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....

Commander

05-25-2002, 02:50 PM

a^2 = b^2 + c^2 - (2bc)cos(A)

this is the cosine law

Jet_Master

05-25-2002, 06:48 PM

dont worry too much if you dont understand it...

you dont need it till at least a couple years... and you will learn it in detail in grade 10.

just wait it out

Commander

05-25-2002, 07:43 PM

good advice!, but didn't u hear the kid? he want's to know it NOW, so he could get ahead of the class

( I learned sin and cos in the begining of gr 8 though ) but one thing jet_master said was true....wait it out....it gets easier the older u get :D

Xterria

05-26-2002, 11:08 AM

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

dbaryl

05-26-2002, 01:07 PM

Well, say you know that the side opposite an angle is 2 and the hypotenuse is 5, this means that sine (opposite/hypotenuse) is 2/5 or 0.4. Now, to find the angle measure all you do is use the inverce function of sine, (written as sin-1).

What we know:

sin (angle) = 0.4

(angle) = ?

(angle) = sin-1 (0.4)

In a scientific calculator, the values for sine of all the angles are stored, so this is essentially asking for the angle whose sine is 0.4. Most of the time you press the [shift] or [2nd] key + [sin] key to get to [sin-1]

Like so: [shift] [sin] [0][.][4] [=] 23.578 degrees.

So, we know that each angle has it's own ratio for sine, cosine and tangent. While we could (theotetically) memorize all these values, the calculator does it for us. In order to get to the angle from sin, cos or tan you just use the inverse functions [sin-1, cos-1 or tan-1]. These are also referred to as arcsine, arccosine, arctangent [arcsin, arccos, arctan], same function, different name.

Shiro

05-26-2002, 01:13 PM

>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.

toaster

05-27-2002, 12:50 PM

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.

Dual-Catfish

05-27-2002, 01:52 PM

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)

stevey

05-27-2002, 02:11 PM

seven old horses, clumsy and heavy, trod on albert.

Procyon

05-27-2002, 02:38 PM

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.)

float t;

for (t = 0; t < 3.14 * 2; t += 0.01)

{

putpixel(200 + cos(t),200 + sin(t));

}

float t;

for (t = 0; t < 3.14 * 2; t += 0.01)

{

putpixel(100 * t, 200 + 100 * sin(t));

}

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));

}

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));

}

fyodor

05-27-2002, 03:07 PM

Questions like, Prove:

sin(x) + 1 - cos(x)sec(x) = cos^3(x)

It does not work out. It simplifies to sin(x)+1=cos^3(x):)

I would also advise you to wait. As someone said, you get incredibly sick of them incredibly fast. Trig is pretty boring stuff until you get to calculus.

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