# Thread: Matrix problem involving trig functions

1. ## Matrix problem involving trig functions

Describe in words what happens graphically to a point (x,y): you must pick at least 3 different angle values (acute/obtuse) or more with the same point until you see a pattern.

[cos x -sin x] * [x] = [x,]
[sin x cos x] * [y] = [y,]

That is a matrix with trig functions times a matrix with the x and y coordinates equals a matrix with the new x and y coordinates)

I have no idea how to do this problem and I REALLY need to know the answer tonight

2. So, I think the most important thing for you to do at this point is to choose angles to input for theta (I'm hoping inside the parentheses, you are supposed to have theta and not x). Once you pic the angles, I suggest picking an (x,y) that are easy to see.
For example, for theta=pi and (1,2)=(x,y), you have...

[cos(pi)*1-sin(pi)*2]=[x']
[sin(pi)*1-cos(pi)*2]=[y']

That's what happens under a 180 degree angle. (Which isn't a terrible amount of an angle.) What about if theta is 45 degrees? 90 degrees? 135 degrees?

3. yes that x was intended to be a theta. know i have graphed it out for many different values and am unable to find the corralation

4. Why don't you try plotting it all for the same point x and y, where x does not equal y? I suggest pi, pi/2, -pi/2, -pi at least. You will find that they trace out a very nice shape if you begin to connect the points

5. Does it make a circle? i am starting to see a curve.

I am also found that if i drew a triangle using the original point, the found point and the origin then the angle at the origin = theta. However i am not sure if this is just a coinsidence

6. There you go! It's actually not a coincidence. It is very much so what happens. What can you say about the radius of what is being formed?

7. Thank you very much! You have been very helpful