Differential Geometry exam confusion!

Right, I need to show that a(t)=(cost,sint,0)is not a geodesic of the plane.

But I'm not sure what I'm supposed to actually do!

Right I've been thinking about the following

a regular curve on a surface is a geodesic of the surface is

a''_(tan)=0?

So I need to get the unit tangent vector field to a(t)? which is

a'(t)/||a'(t)|| so

a'(t)=(-sint,cost,0) and ||a'(t)||=ROOT(sin^2(t)+cos^2(t))=1

so T(t)=(-sint,cost,0)

Now a''_tan(t)=(a''.T)T+(a''.(TXn)TXn)

n=(PHIu X PHIv)/||PHIu X PHIv||

I'm not sure where I'm going from here on in, I end up completely

confused with tons of definitions? Am I on the right track?

Any help much appreciated!