# Graphing polar coordinates

## 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

## 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.

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.