Understanding The Electric Flux of A Cube Rotated by an Angle Theta

[mrrocketknigh]

Hey, all, so I have been studying this problem all morning, and I do not understand two aspects to this example problem. I included a photo of the diagram used in this problem. You will see two cubes, but the diagram which corresponds to the problem below is the one on the right.PROBLEM: Find the electric flux through each face of the cube and the total flux of the cube when the cube is turned by an angle theta.https://www.physicsforums.com/attachments/65421

Below both diagrams in the photo is the answer given; they are the respective fluxes of each side of the cube. What I don't understand is how for n3 the flux is equal to E(L^2)cos(90* + THETA) = - E(L^2)sinTHETA .

I tried finding why the cosine is also equal to the negative sine in this problem, but to no avail. If someone can help me gain a new or more efficient perspective so that I can see the logic of the problem, I would greatly appreciate it. The flux of a uniform electric field, is:
FLUX = E (A*n) cosTHETA. where E is the magnitude of the strength of the electric field, A is the area of the cube, n is the direction of the normal vector to side of the cube, and THETA is the angle the cube was turned ( this I am not completely sure on, if I am wrong then please correct me).

Cheers,

MrRocketKnight

 

[Simon Bridge]

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What I don't understand is how for n3 the flux is equal to E(L^2)cos(90* + THETA) = - E(L^2)sinTHETA .
I tried finding why the cosine is also equal to the negative sine in this problem, but to no avail.

It's a trig identity.
http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities
cos(A+B)=cosAcosB - sinAsinB