Question

Can someone help me with this calc bc work for #13

Answer 1

The horizontal axis for each graph is the value of t. It represents which moment in time we're at.

The vertical axis for the left and right graphs are the x and y coordinates respectively.

At time t = 0, we have x = 0 pair up with y = 1. Therefore, the particle starts at the location (0,1).

At time t = 1, we now have x = 1 pair up with y = 0. The particle is at location (1,0) at time t = 1.

Repeat this process until reaching t = 4.

Here's a table of values

`\begin{array} \cline{1-2}t & (x,y)\\\cline{1-2}0 & (0,1)\\\cline{1-2}1 & (1,0)\\\cline{1-2}2 & (0,-1)\\\cline{1-2}3 & (-1,0)\\\cline{1-2}4 & (0,1)\\\cline{1-2}\end{array}`

We go from (0,1) to (1,0) then to (0,-1) and next to (-1,0) before arriving at (0,1) once again.

The particle takes a clockwise journey starting at (0,1) and ends up back at (0,1) when t = 4.

This motion is somewhat similar to the periodic motion found on the unit circle.