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so we now have vector subtraction so when we subtract this location from this location itamp;#39;ll give us this vector we have perp counterclockwise so i can take this thing and rotate it 90 degrees that direction and then again we have vector subtraction so i can subtract the shipamp;#39;s position from the same origin vector as we did with this one where we subtracted this vector from that to get that vector and then weamp;#39;re going to subtract this point or vector from the ship position to get that vector and then we can say hey whatamp;#39;s whatamp;#39;s the dot product between the two thatamp;#39;ll tell me the magnitude of each of them times the cosine of the angle but i donamp;#39;t care about any of that all i care about is the sine of the cosine of the angle and if the sine is positive i know that we are in this range which is fine zero up to 90 degrees weamp;#39;re fine in that case but once we go negative we know that the cosine of the angle is negative and wea