What is the best trick to be able to draw all polar curves within 5 minutes?...

What is the best trick to be able to draw all polar curves within 5 minutes? Please provide detailed clarification and some examples.

Solutions

Expert Solution

Let's take an example

R=4 cos t

This is the equation we r solving and find the graphs

Solution

We first construct a table of values using the special angles and their multiples .

It is useful to first find values of the that makes R maximum, minimum or equal to zero .R is maximum or equal to 4 for t = 0.R is minimum and equal to -4--4 for t =pi and R is equal to zero for t = pi/2.

stop the calculation at t= pi because the values will repeat

now plot the above points on a system of polar coordinates. First you need to understand the plotting of points in polar coordinates before you go any further .A system of polar coordinates with R = constant and t= constant.

And you need to pay the special attention to point with negative values of R.

Now join the points drawing smooth curve.

milcah answered 1 year ago

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