Find angular speed of a point on the earth

[suspenc3]

what is the angular speed \Omega about the polar axis of a point on Earth's surface at a latitude of 40^o

I know that the radius of the Earth is 6.37 x 10^6m

I also know that the Earth rotates about this axis (40^o)

What do I do?

 

[mezarashi]

This is geometry. Draw a circle, and mark an angle of 40 degrees (this is equivalent to lattitude of 40). What is the x component? This is the component that 'effectively' participates in the circular motion.

Edit: If it's the angular velocity you are looking for, you'll find that it will be the same regardless of lattitude.