Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
up vote 2 down vote accepted

A sinusoid is a function which can be written in the form $f(x) = R\sin (ax + b)$. So for example $\cos x = \sin (-x + \frac{\pi}{2})$, and so forth.

It sounds like your sinusoidal spiral is a generalisation of this: Wikipedia page has more information.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.