Polar curves

[Axioms]

The question

r = 1 + sint

Find the points on the cardioid where the tangent line is horizontal or vertical.

 

I get dy/dt = (cost (1+2sint)) = 0

and dx/dt = (1+sint)(1-2sint) = 0

 

I can see for dy/dt you get pi/2, 3pi/2, 7pi/2 and 11pi/6

and for dx/dt you get 3pi/2, pi/6 and 5pi/6

 

I am struggling to remember how to find the r coordinates of this. Do you substitute the points back into the original equation?

You find (2, pi/2) ; etc.

 

I just need to know if that is how you would get the r coordiante.

 

If someone can help it would be appreciated.

 

 

[Xittenn]

Plot your guess and confirm? You should be able to check this on a graphing calculator.

 

On the ti-83 trace with a polar graph still gives the x and y coordinates which is sucky . . . . . but easily converted to r . . . . :/

[Axioms]

I have and it seems to be correct. I dont have a graphing calculator with me though.

[Xittenn]

I have and it seems to be correct. I dont have a graphing calculator with me though.

 

Graphing calculators are handy things!