Symmetry of cardioid in parametric equation

Question

The parametric equation of cardioid is $$(x(t),y(t))=(a(2\cos t-\cos 2t), a(2\sin t-\sin 2t)).$$ How To underdstand from parametric equation that this curve is symmetric about $x$-axis?

Can anyone explain that in detail?

Answer 1

By the parity of the functions, $(x,y)$ and $(x,-y)$ are reached for $t$ and $-t$.