Help….?!?!???!?!

Question

Draw the arrows on the following graph to represent the orientation of the following parametric equation

x(t)=3cos1/2t

y(t)=-5sin1/2t

https://drive.google.com/file/d/1jxrkF1JLlNo-50Uz24ucjWNxm2hAWxPc/view?usp=drivesdk

explain how you solved please

Answer 1

The orientation is the direction in which the graph is traced out. To determine the orientation, you can plug in a few different values of t to find the corresponding points.

You can think of t=0 as the starting point.

When t=0, then x=3cos(0)=3 and y=-5sin(0)=0. So the starting point is (3,0), on the right-hand side of the ellipse.

Then, choose a higher value of t to see where the particle is traveling. Since the parametric functions are trig functions, let's consider t=pi. At this point x=3cos(pi/2)=0 and y=-5sin(pi/2)=-5. So, t=pi corresponds to the point (0, -5), on the bottom of the ellipse.

From this, you can conclude that as t increases, the curve is traced out in a counterclockwise direction.