Answer
The points of intersection of $y_1$ and $y_2$ are:
$( \frac{\pi}{2}+2\pi~n, e^{-\frac{\pi}{2}-2\pi~n})$
The t-coordinates of the points of intersection of $y_1$ and $y_2$ are the same as the x-coordinates where the graph of $~~y = sin~x~~$ has a value of $1$
The points of intersection of $y_1$ and $y_3$ are:
$( \frac{3\pi}{2}+2\pi~n, -e^{-\frac{3\pi}{2}-2\pi~n})$
The t-coordinates of the points of intersection of $y_1$ and $y_3$ are the same as the x-coordinates where the graph of $~~y = sin~x~~$ has a value of $-1$
Work Step by Step
$y_1 = e^{-t}~sin~t$
$y_2 = e^{-t}$
We can find the t-coordinates of the points of intersection:
$y_1 = y_2$
$e^{-t}~sin~t = e^{-t}$
$sin~t = 1$
$t = \frac{\pi}{2}+2\pi~n,~~$ where $n$ is an integer
The points of intersection of $y_1$ and $y_2$ are:
$( \frac{\pi}{2}+2\pi~n, e^{-\frac{\pi}{2}-2\pi~n})$
The t-coordinates of the points of intersection of $y_1$ and $y_2$ are the same as the x-coordinates where the graph of $~~y = sin~x~~$ has a value of $1$
$y_1 = e^{-t}~sin~t$
$y_3 = -e^{-t}$
We can find the t-coordinates of the points of intersection:
$y_1 = y_3$
$e^{-t}~sin~t = -e^{-t}$
$sin~t = -1$
$t = \frac{3\pi}{2}+2\pi~n,~~$ where $n$ is an integer
The points of intersection of $y_1$ and $y_3$ are:
$( \frac{3\pi}{2}+2\pi~n, -e^{-\frac{3\pi}{2}-2\pi~n})$
The t-coordinates of the points of intersection of $y_1$ and $y_3$ are the same as the x-coordinates where the graph of $~~y = sin~x~~$ has a value of $-1$