What is the speed of the Earth's rotation?

At the equator, the circumference of the Earth is 40,070 kilometers, and the day is 24 hours long so the speed is 1670 kilometers/hour ( 1037 miles/hr). This decreases by the cosine of your latitude so that at a latitude of 45 degrees, cos(45) = .707 and the speed is .707 x 1670 = 1180 kilometers/hr. You can use this formula to find the speed of rotation at any latitude.

BTW: make sure that when you use your calculator that you set up the arguments for the trig functions in terms of degrees not radiane!