Find the equation of each tangent to the curve $r=a\cos3\theta$ which is parallel to the initial line(horizontal axis).
here is my steps: $y=r\sin\theta=a\cos(3\theta)\sin\theta$
$dy/d\theta=a(\cos\theta\cos(3\theta)-3\sin(3\theta)\sin\theta)=0$.
I tried to use Product-to-Sum formula
->$\frac{1}{2}(\sin(π/2+2\theta)-\sin(π/2-4\theta))-\frac{3}{2}(\sin(π/2+2\theta)+\sin(π/2+4\theta))=0$
then I don't know how to continue..