Question 47978
1. cot, {{{cot(-pi/2)=(cos(-pi/2)/sin(-pi/2))}}}, {{{cos(-pi/2)=0}}}, {{{sin(-pi/2)=-1}}}, then {{{cot(-pi/2)= 0}}}
2. {{{sin(5pi/6)}}} has a reference angle of {{{pi/6}}}} and in Quadrant 2. sin is negative in Quadrant 2.  {{{sin(pi/6)=1/2}}}, so {{{sin(5pi/6)=-1/2}}}.  
Take the square of {{{(-1/2)^2}}} gives us 1/4
3. {{{Sec(11pi/6)}}} has a reference angle of {{{pi/6}}} and in Quadrant 4. Sec is positive in Quadrant 4.  {{{sec(pi/6)=1/cos(pi/6)}}} and {{{cos(pi/6)=(sqrt(3))/2}}} then {{{sec(pi/6)=2/(sqrt(3))}}}
Squaring it gives {{{(2/(sqrt(3)))^2=4/3}}}
4. {{{sec^-1(sec(-30degrees))= 30  or -30 degree}}}
{{{sec(-30degree)= 2/(sqrt(3))}}}
{{{sec^-1(2/(sqrt(3)))= 30  or -30 degree}}}
since in both Quadrant 1 and 4, sec(-30degree) is positive