From the unit circle, we know that: cos(3pi/2) = 0 and sin(3pi/2) = -1, we recover that
cos(-4+3pi/2) = sin(-4)
Therefore, when we take the arccos of both sides we get:
arccos( cos(-4+3pi/2)) = arccos(sin(-4))
And on the left hand side, the arccos and the cos cancel giving:
-4 + 3pi/2 = arccos(sin(-4))
*Note: the range of the arccos function is from -1 to 1, therefore we need to make sure that the output we get is in that range. In this case, we see that -4+3pi/2 = 0.712..., which is between -1 and 1. So final answer is -4+3pi/2
Please let me know if you need any clarification. Always glad to help!