The goal is to eliminate
and
from the equation and introduce
and
Ideally, we would write the equation
as a function of
To obtain the polar form, we will use the relationships between
and
Since
and
we can substitute and solve for
Thus,
and
should generate the same graph. See
[link] .
(a) Cartesian form
(b) Polar form
To graph a circle in rectangular form, we must first solve for
Note that this is two separate functions, since a circle fails the vertical line test. Therefore, we need to enter the positive and negative square roots into the calculator separately, as two equations in the form
and
Press
GRAPH.
Rewriting a cartesian equation as a polar equation
Rewrite the
Cartesian equation
as a polar equation.
This equation appears similar to the previous example, but it requires different steps to convert the equation.
We can still follow the same procedures we have already learned and make the following substitutions:
Therefore, the equations
and
should give us the same graph. See
[link] .
(a) Cartesian form
(b) polar form
The Cartesian or
rectangular equation is plotted on the rectangular grid, and the
polar equation is plotted on the polar grid. Clearly, the graphs are identical.
Rewriting a cartesian equation in polar form
Rewrite the Cartesian equation
as a polar equation.
We will use the relationships
and
Rewrite the Cartesian equation
in polar form.
Identify and graph polar equations by converting to rectangular equations
We have learned how to convert rectangular coordinates to polar coordinates, and we have seen that the points are indeed the same. We have also transformed polar equations to rectangular equations and vice versa. Now we will demonstrate that their graphs, while drawn on different grids, are identical.
Graphing a polar equation by converting to a rectangular equation
Covert the polar equation
to a rectangular equation, and draw its corresponding graph.
The conversion is
Notice that the equation
drawn on the polar grid is clearly the same as the vertical line
drawn on the rectangular grid (see
[link] ). Just as
is the standard form for a vertical line in rectangular form,
is the standard form for a vertical line in polar form.
(a) Polar grid (b) Rectangular coordinate system
A similar discussion would demonstrate that the graph of the function
will be the horizontal line
In fact,
is the standard form for a horizontal line in polar form, corresponding to the rectangular form
Questions & Answers
I'm interested in biological psychology and cognitive psychology
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills