Please tell me how we sketch polar curve in Polar Coordinates..

I attach the Document about some questions related to above heading.

Please tell me its solution with step by step..

Please tell me as soon as possible..

Thanks too much. God Bless you..

When you do these plots, treat r as the dependent variable and as the independent variable. In other words, choose a value for , then solve for the resulting value of r.

In this particular case, all of your equations include an extra constant a. This could be any number, so it's best to account for it by simply drawing your polar axes in terms of a, like in the attached picture. Note that I've labelled the radius coordinates in black (and they're in terms of the number a) and the angle coordinates in red.

So to do the first one, , start by choosing various values of , then solve for r. For example, let's choose ; that results in . So you'd plot a point at , which is the origin at the center of the plot. How about ? That results in . So you'd plot a point at , which is along the line segment pointing at the label on the graph, a little less than a units out from the center (about 0.785a). In other words, just inside the smallest circle on the graph.

Continue plotting points in this fashion until you have enough to connect the dots and draw your graph.

Note that I only labelled the angles from 0 to just under 2, but in reality the angle wraps around again and again at 2, 4, 6, etc.

Note that in the second problem, you'll have to do a little algebra to get to the other side of the equals sign so you can have r all by itself. Other than that, it's the same process (although you may find that you need to adjust your radius scale a little so that concentric circles are in increments of, say, 0.1a or something).

Hm... nice set of curves. They are fascinating! Thanks for having asked that question Wikkibahi :)