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# FUN STUFF: Describe the motion of a particle?? help! (calc)?

Describe the motion of a particle with position (x, y) as t varies in the given interval.

x = cos^2(t), y = cos t, 0<= t<= 4

and its fill in the blank:

The particle moves along the parabola x = y2. As t goes from 0 to 4, the particle moves from ( , ) down to ( , ) (at t = ), back up to ( , ) again (at t = 2), and then repeats this entire cycle between t = 2 and t = 4.

s

I know you just make a chart, pluging in values of t. But for example, how do you solve x=cos^2(0)?? without calculator, or even with calculator?

### 1 Answer

- supersonic332003Lv 71 decade agoFavorite Answer
I'll start with your example:

The trigonometric numbers for certain angles are considered as known

(you can imagine the unit circle == a circle with radius 1, the center of which is at the beginning of the system of coordinates. Then, for each point (x,y) on the circle, x=cosu, y=sinu, where u is the angle between the x axis and the radius to (x,y), measured counterclockwise).

You also have to keep in mind that

cos^2 u + sin^2 u = 1 and -1<=sinu<=1, -1<=cosu<=1.

For the trig. numbers you cannot calculate easily, I guess it's just enough if you say, e.g. sin(3).

P.S. if it helps, sint is a periodic function with a t period equal to 2pi.