# Calculus

posted by .

the path of a particle in the xy-plane is vector r = (cos2t, sint) for t for all [-pi/2, pi] where t represents time. Sketch the path. Is it a smooth curve?

How do i sketch the path? do i just plug in random points between [-pi/2, pi]? how would i connect it together? and how do i know if it's a smooth curve? Thank you.

• Calculus -

If that pair of coordinates represents (X,Y), then the easiest way is to do pretty much what you already suggested, but do it systematically in small increments. That is, work out a set of points as follows. -pi/2 is approximately -1.57, so

t=-1.57, X=cos(2t)=-1, Y=sin(t)=-1
t=-1.4, X=cos(2t)=-0.942, Y=sin(t)=-0.985
t=-1.3, X=cos(2t)=-0.856, Y=sin(t)=-0.963
etc etc. Then just plot X vs Y. If you've got access to a spreadsheet you'll find it very quick to do that.

Just one question though: are you sure that interval isn't [-pi/2, +pi/2]? If so, then yes, it's a smooth curve between those limits. But if you're correct about the upper limit for t being pi, then the curve is rather more complicated: it runs smoothly from (-1,1) through (0,0), up to (-1,1) and then bounces back on itself again to (0,0), overwriting itself in the process. If I had to bet, I'd guess that the question has been copied down wrong.

## Similar Questions

1. ### Calculus

A small aircraft starts its descent from an altitude of 1 mile, 4 miles west of the runway. a) Find the cubic f(x) = ax3 + bx2 + cx + d on the interval [-4,0] that describes a smooth glide path for the landing. b) If the glide path …
2. ### calculus

A particle traces the path vector r = (t^3, t+3, t^2 -4t) where t represents time; it flies off on a tangent when t=1 and then moves in a straight line with constant speed. Find its position when t=4. Do I just plug the 4 into the …
3. ### calculus

the path of a particle in the xy-plane is vector r = (cos2t, sint) for t for all [-pi/2, pi] where t represents time. Sketch the path. Is it a smooth curve?
4. ### math

A particle is traveling along a one-dimensional path (such as a number line). The position of the particle is governed by the time function x(t) ƒ­ 3t 4 ƒ{16t3 ƒy18t 2 ƒy 2 , where t is in minutes and 0 „T t „T 5 . Answer …
5. ### Physics

A straight path is inclined at an angle of 15 degree to the horizontal. A loaded skip of total mass 1500 kg is at rest on the path and is attached to a wall at the top of the path by a rope. The rope is taut and parallel to a line …
6. ### physics

The position vector r of a particle moving in the xy plane is r=2ti+2sin[(pi/4)t]j , with is in meters and t in seconds. (a) Calculate the x and y components of the particle's position at , and 4.0 s and sketch the particle's path …
7. ### help~MATHS

Let S be the set of {(1,0),(0,1),(1,1),(1,−1),(−1,1)}-lattice path which begin at (1,1), do not use the same vertex twice, and never touch either the x-axis or the y-axis. Let Px,y be the number of paths in S which end …
8. ### sd224

Let S be the set of {(1,0),(0,1),(1,1),(1,−1),(−1,1)}-lattice path which begin at (1,1), do not use the same vertex twice, and never touch either the x-axis or the y-axis. Let Px,y be the number of paths in S which end …
9. ### Geometry

A scientist is plotting the circular path of a particle on a coordinate plane for a lab experiment. The scientist knows the path is a perfect circle and that the particle starts at ordered pair (-5, -11). When the particle is halfway …
10. ### Pre Calculus

A park has a circular walking path with a diameter of 250 meters. a) Write the equation to describe the walking path in your diagram. b) Find the distance traveled by someone walking once around the entire path. c) Find the distance …

More Similar Questions