Rewrite the polar equation
as a Cartesian equation.
The goal is to eliminate
and
and introduce
and
We clear the fraction, and then use substitution. In order to replace
with
and
we must use the expression
The Cartesian equation is
However, to graph it, especially using a graphing calculator or computer program, we want to isolate
When our entire equation has been changed from
and
to
and
we can stop, unless asked to solve for
or simplify. See
[link] .
The “hour-glass” shape of the graph is called a
hyperbola . Hyperbolas have many interesting geometric features and applications, which we will investigate further in
Analytic Geometry .
The polar grid is represented as a series of concentric circles radiating out from the pole, or origin.
To plot a point in the form
move in a counterclockwise direction from the polar axis by an angle of
and then extend a directed line segment from the pole the length of
in the direction of
If
is negative, move in a clockwise direction, and extend a directed line segment the length of
in the direction of
See
[link] .
If
is negative, extend the directed line segment in the opposite direction of
See
[link] .
To convert from polar coordinates to rectangular coordinates, use the formulas
and
See
[link] and
[link] .
To convert from rectangular coordinates to polar coordinates, use one or more of the formulas:
and
See
[link] .
Transforming equations between polar and rectangular forms means making the appropriate substitutions based on the available formulas, together with algebraic manipulations. See
[link] ,
[link] , and
[link] .
Using the appropriate substitutions makes it possible to rewrite a polar equation as a rectangular equation, and then graph it in the rectangular plane. See
[link] ,
[link] , and
[link] .
Section exercises
Verbal
How are polar coordinates different from rectangular coordinates?
For polar coordinates, the point in the plane depends on the angle from the positive
x- axis and distance from the origin, while in Cartesian coordinates, the point represents the horizontal and vertical distances from the origin. For each point in the coordinate plane, there is one representation, but for each point in the polar plane, there are infinite representations.
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.