I have question related with these two definition: In geometry, the sinusoidal spirals are a family of curves defined by the equation in polar coordinates
$$r^n = a^n \cos(n \theta)$$
where $a$ is a nonzero constant and $n$ is a rational number other than $0$. On the other hand, with a rotation about the origin, this can also be written
$$r^n = a^n \sin(n \theta)$$
Why so different? Rotation about the origin does create in some situation cosine and sine function same or? Please explain to me.