Newtons Laws with Uniform Circular motion

[lubuntu]

Homework Statement

An airplane is flying in a circle at a speed of 480km/h. It wings are tilted at 40 degrees to the horizontal. What is the radius of the circle in which the plane is flying? Assume that the required for is entirely provided by "aerodynamic life" that is perpendicular to the wings.

Homework Equations

f=ma a=v^2/r

The Attempt at a Solution

I tried this and got what seems like a reasonable answer but the books answer guide differs, what am I missing here?


for the X direction i get

N cos(40) = mv^2/r

for the Y direction I get

N sin(40) - mg = 0


so...
N = mg/sin(40)


Substituting back and solving for r

r = (v^2 tan(40))/g

What am I missing?

 

[lubuntu]

Figured it out I swapped the sin and the cos, does anyone know a good way of keeping track of which should be used where, I seems to run into trouble with it once in awhile.

 

[AEM]

Figured it out I swapped the sin and the cos, does anyone know a good way of keeping track of which should be used where, I seems to run into trouble with it once in awhile.

I make a practice of drawing a careful picture and working off of that to determine which trig function to use rather than trying to find some "rule" that will "work in all situations".