The basic idea of finding the tangent line of a graph that is using the polar coordinate system as opposed to the Cartesian system is basically by finding a point and a slope like you would with normal equations. However instead of simply taking the derivative of an equation you have to do a little bit more work.
This is the most important equation when trying to find the tangent line. This equation is basically using the derivatives of the equations for crossing between the polar and cartesian planes, the equations being
and
so in order to find an equation at a point you will be given an equation in polar form and a point that you want to find it at.
at
All you have to do is take the derivative of that equation with respect to theta and use that to plug it into the master formula. Once you simplify it down to a more manageable equation you then plug in
and solve to get your slope. Then to find a point you will need to plug in
into the original equation that you had. This will give you an "r" value that then finally you just need to take the crossing over equations and put in the r value and the initial condition in and solve which will give you an x and y point.
and
this will give you a Cartesian set of points and a slope and all you have to do from there is plug it into the equation
That is all you have to do.
For more help on this subject you can go to this site.
For more help on polar equations in general you can go to here.
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