Graphing a Polar Function: Solving for r = 2cosθ

[physicsnewb7]

Homework Statement

graph the polar function r=2cos\theta (-\pi/2 \leq \theta \leq \pi/2) sorry that last theta/2 should be pi/2. new to this math text

Homework Equations

The Attempt at a Solution

I graphed the positive part right, I think. it seems to trace a half circle. I get confused when it comes to the negative radians. what would this trace out in full. Excuse me but its been a while since trig.

 

[gabbagabbahey]

You should get a full circle of unit radius, centered at (1,0). The easiest way to see that \frac{-\pi}{2}<\theta<\frac{\pi}{2} traces out the entire circle is to find parametric equations for x-1 and y and use the double angle identities. You should find that x-1=\cos(2\theta) and y=\sin(2\theta) and so as theta moves through pi radians, (x-1) and y both move through a full period, tracing out the entire circle.

 

[Hogger]

I think an even easier way once you find part of the graph is use symmetry. If you can replace theta by negative theta then there is symmetry with respect to the polar axis and the circle is completed.