doc3232 explained it correctly:

cos(Pi + 301Pi/2) is equivalent to cos(150Pi + 3Pi/2)

since 2Pi is just 360 degrees, it doesn't affect the answer, therefore:

150Pi/2Pi = 75.

that is 75 "loops" or, 75 three sixty degree spins. so now you can drop that term completely out of the problem, and you have:

cos(3Pi/2)

which is just 1.5Pi, which is equivalent to 270 degrees, or, pointing straight down south. and when you're pointing down south, cos = 0.

but I got another problem for you.

Sec^2 (A) + Tan^2 (A-3) = 0

apparently the answer is (pi/4) but I'm not 100% sure of that cuz it don't make any sense!!! I've been lookin at this problem and trying to figure it out for a month now. still can't get it...

I just attempted it again and got stuck here:

1 = tan^2 (A-(Pi/60)) - tan^2 (A)

1 = tan (A) [tan (1-(Pi/60A)) - tan (Pi/180)]

I don't know if anything I'm doing is correct by the way. I'm not even sure if I can convert that "A-3" into radians from the beginning...