find the exact value of cot(9π/2) and sin(-5π) ???

Why not use the fact that functions sin/cos and tan/cot are periodic (reach same values) every (multiple of π) and thus cot(9×π/2) = cot[ 8×π/2 + π/2 ] = cot[ 4×π + π/2 ] = cot( π/2 ) = cos( π/2 )/sin( π/2 ) = 0.

On the other hand sin(-5π) = sin( 0 - 5×π ) = sin ( 0 ) = 0.