Thread: sin and cosin

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

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

Code:

  |\
  |  \
  |    \ 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

Code:

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-

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 ......

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

Code:

      |\
      |  \
      |   \ y = 20
x=?|     \
      |___\
      z = 10

how would I use sin/cosine to find x?
thanks

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.

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

Code:

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

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