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I current picked up Fundamentals of Aerodynamics by John D. Anderson Jr. and am having a little bit of trouble understanding some of the equations i am given. This is the first aero book ive picked up so im not too familiar with aero concepts or terms yet.

On page 20, they break down the Lift and Drag components geometrically. The symbols below are as follows: A= axial force and N=normal force. [tex] \alpha = [/tex] angle of attack.

They have:

[tex]L=N\cos \alpha - A\sin \alpha [/tex]

[tex]D=N\sin \alpha + A\cos \alpha [/tex]

I am having trouble understanding why this is true, and why they put the +/- where they did. I see that [tex]N\cos \alpha [/tex] is equal to L, so why are we subtracting the [tex]A\sin \alpha [/tex] ? Same goes for the equation for D. Im sure im overlooking something very obvious here, but id appreciate someone helping me see it.

Thanks.