# algebra precalculus – How fast are you moving on the earth at a given latitude?

If you’re standing at a latitude of $$theta^{,circ}$$, then you’re rotating on a circle of radius $$Rcos(theta)$$, where $$R = 3959,mathrm{mi}$$ is the radius of the earth. This circle still does one revolution in (about!) $$24,mathrm{hrs}$$, so we can calculate the speed from there.

$$left(frac{1}{24 ,mathrm{hours}}right) times 2pi Rcostheta ,mathrm{miles} approx 1036costheta ,mathrm{mph}$$

So you’ve just gotta scale the speed at the equator by $$costheta$$.