Draw the graph polar coordinates

Question

Draw the graph $r=3\cos a$ and write me how do you this? Show me polar coordinates system $a=360°$.

Answer 1

$$r=3\cos\alpha\\x=r\cos\alpha\\y=r\sin\alpha$$ From here $$y=3\sin\alpha\cos\alpha=\frac 32\sin(2\alpha)\\x=3\cos^2\alpha=\frac 32\cos(2\alpha)-\frac 32$$ Moving the last term in $x$ to the left hand side, squaring the two equations, and summing them, you get $$\left(x-\frac 32\right)^2+y^2=\left(\frac32\right)^2$$ This is the equation of a circle with radius $1.5$ and center at $(1.5,0)$