Chicken6, thanks for the comment about sine and cosine. I agree with you. Please excuse my poor English. Let me try again.
Induced drag is the by-product of lift. The resultant force on an airfoil is slightly slanted backward (due to bending of the airflow around the airfoil), this backward force is the induced drag. The more pronounced the bending of airflow the greater the induced drag. Induced drag is proportional to sine of the effective angle of attack of the airfoil. When airspeed increases, AOA decrease, and induced drag also decrease.
Induced drag does not include drag caused by resistant to movement of airfoil through the air.
Is it clearer now ?
p/s: Some people would not include wing-tip vortices as part of induced drag, although they are closely related. One of the argument is: when AOA is zero, lift is zero, then induced drag would also be zero. But wing-tip vortices is not zero (low, but not zero). When no lift is produced (or desired), all the drag on this airfoil is profile drag.
[This message has been edited by Old Dog (edited 22 November 2000).]