Hummm... let's see...
cos // sin 23.00º = 0.92050485345 // 0.39073112848
cos // sin 23.01º = 0.92043664398 // 0.39089178094
Now image I have a vector, DistEarthMoonBase with magnitude 384400000 meters.
At 23.00º, the Moon Base is at
(x, y): 384400000*0.92050485345, 384400000*0.39073112848 <=>
(x, y): 353842.065666, 150197.045788 kilometers
At 23.01º, the Moon Base is at
(x, y): 384400000*0.92043664398, 384400000*0.39089178094 <=>
(x, y): 353815.845946, 150258.800593 kilometers
deltaX = 26.219720
deltaY = 61.754805
Distance given by Sqrt(deltaX^2 + deltaY^2): 67.090 Kilometers
So... if you're sending a spaceship to a lunar base at 23.01º, but you opt to discard the 0.01º, you'd miss the target by 67 kilometers.