Slopes of Tangent Lines of Polar Equations

a) Find all points where the following curves have vertical and horizontal tangent lines.
b) Find the slope of the lines tangent to the curve at the origin (when relevant)
c) Sketch the curve and all the tangent lines identified in parts (a) and (b).2\theta

$$r = 2\cos(2 \theta)$$

Question

Slopes of Tangent Lines of Polar Equations


a) Find all points where the following curves have vertical and horizontal tangent lines.
b) Find the slope of the lines tangent to the curve at the origin (when relevant)
c) Sketch the curve and all the tangent lines identified in parts (a) and (b).2\theta

$$r = 2\cos(2 \theta)$$

abb0t · Answer

slope of tangent means derivative. find it for $\large \frac{dr}{d \theta}$

austinl · Answer

I know how to find a slope.... I need to figure out on the graph where these points are.

abb0t · Answer

You could convert it to cartesian coordinates (x,y) to make it easier to graph.

austinl · Answer

|dw:1374615201527:dw|
It looks similar to this, devilishly hard to graph well on here.

fibonaccichick666 · Answer

maybe think about, when does the derivative =0? and how many radians before it repeats itself

austinl · Answer

That, that actually helped.

fibonaccichick666 · Answer

happy it did :)

austinl · Answer

Ok, so I have...
Vertical: (2,pi/2),(2,3pi/2)
Horizontal: (2,0),(2,pi)
This correct?

fibonaccichick666 · Answer

What about for $(\infty, \infty)$?

fibonaccichick666 · Answer

sorry (-∞,∞)