Question $3(3$ points$)$

The following Python code plots i $=1$ e

s$1$

$2$ on the interval $0<=$ s $<=1.$ It

plots a red dashed line, adds a label in a legend, and uses half of the figure $($one

subplot out of two$).$

import numpy as np

import matplotlib.pyplot as plt

s $=$ np$.$linspace$(0,1,2**7)$

i $=1-$ np$.$exp$($s $-0\mathrm{.}5)$

plt$.$subplot$(1,2,1)$

plt$.$plot$($s$,$ i$,"$r$--",$ label$="$i$")$

plt$.$legend$()$

plt$.$xlabel$($s$)$

plt$.$show$()$

a$)$ On the same subplot, plot j $=$ s

$2$

$1$

$4$

and k $=$

$1$

s$+1.$ Make sure all values

are labeled and easily distinguishable from one another.

b$)$ The given values of i$($s$),$ j$($s$),$ k$($s$)$ are Cartesian coordiates of an object

as a function of s$.$ On the same subplot, plot also the radial distance of the

object from the k axis and the radius of the object from the origin.

c$)$ On a second subplot, plot the azimuth $($from the i axis$)$ and the elevation

$($from the k axis$)$ of the object. Make sure all values are labeled and easily

distinguishable from one another.

Hint: read about np$.$arctan$2$ and np$.$arccos functions.