Suppose That the Position of One Particle at Time T $1$

question 16

Short Answer

Suppose that the position of one particle at time t is given by
x $1$ = 4 sin t, y $1$ = 2 cos t for 0 $\leq t \leq 2 \pi$ and the position of a second particle is given by
x $2$ = 2 cos t - 1, y $2$ = 4 sin t + 2 for 0 $\leq t \leq 2 \pi$ (a) How many points of intersection are there for these two paths?
(b) Are any of these collision points (that is, points where the particles are at the same place at the same time)? If so, find the collision points.

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Definitions:

Antagonist

In physiology, a muscle that acts in opposition to the action of another muscle, called the agonist; in pharmacology, a substance that inhibits the action of another substance.

Neuromodulator

A neuromodulator is a substance in the nervous system that modifies the functions of neurons, influencing how signals are transmitted across synapses.

Neurotransmitter

Chemical substances that transmit signals from one neuron to another across synapses, playing key roles in the functioning of the nervous system.

Reuptake

Process by which neurotransmitters are taken back into the synaptic vesicles.