find the pedal equation of r=2a/1+cos theta
Answers
Step-by-step explanation:
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Answer:
Your polar plot should look something like this:
enter image source here
Step-by-step explanation:
The question is asking us to create a polar plot of a function of angle,
θ
, which gives us
r
, the distance from the origin. Before starting we should get an idea of the range of
r
values we can expect. That will help us decide on a scale for our axes.
The function
cos
(
θ
)
has a range
[
−
1
,
+
1
]
so the quantity in parentheses
1
+
cos
(
θ
)
has a range
[
0
,
2
]
. We then multiply that by
2
a
giving:
r
=
2
a
(
1
+
cos
(
θ
)
)
∈
[
0
,
4
a
]
This is the ditance to the origin, which could be at any angle, so let's make our axes,
x
and
y
run from
−
4
a
to
+
4
a
just in case:
Next, it's useful to make a table of the value of our function. We know that
θ
∈
[
0
,
360
o
]
and let's break it up into 25 points (we use 25 because that makes 24 steps between points which are angles of
15
o
):
enter image source here