Question 956408
A.

{{{sin (270) =-1}}} ....recall that angle {{{270}}}° directly across {{{90}}}° on unit circle;  {{{sin(90)}}}° is equal to {{{1}}} then {{{sin(270)}}}° is equal to {{{-1}}}

B.

on unit circle {{{(3pi/2)}}} corresponds to {{{270}}}° 
Let's start with tangent. Tangent at {{{270}}} degrees is {{{infinite}}}. Since {{{cotangent}}} is the reciprocal of {{{270}}}, that means you have to do {{{1/infinite}}}.

{{{infinite = 1/0)}}}, then {{{1/infinite=1/(1/0)= 0}}}, which is your answer. 

so,  {{{cot(3pi/2) =cot(270)=0}}}


or, do it using unit circle (cos,sin) values

we now that {{{cot( 270 ) = cos( 270 ) / sin( 270 )}}}

we can see on unit circle that {{{cos( 270 )=0}}} and {{{sin( 270 )=-1}}}

then {{{cot( 270 ) =0/-1=0}}}