Question 739202
{{{sin(30^o)=1/2}}} {{{cos(30^o)=sqrt(3)/2}}} {{{cot(30^o)=cos(30^o)/sin(30^o)=sqrt(3)}}}
 
No need to memorize that. Just picture an equilateral triangle with side length 1.
All the angles in that triangle measure {{{180^o/3=60^o}}}.
{{{drawing(300,300, -0.3,1.3,-0.65,0.65,
triangle(0,0,0.866,-0.5,0.866,0.5),
green(line(0,0,0.866,0)),green(rectangle(0.866,0,0.836,0.03)),
locate(0.13,0.02,30^o),locate(0.1,0.1,30^o),
locate(0.43,0.25,1),locate(0.43,-0.26,1),
locate(0.806,0.28,1/2),locate(0.806,-0.15,1/2),
locate(-0.06,0.03,A), locate(0.876,0.03,P)
)}}} According to the Pythagorean theorem, {{{1^2=(1/2)^2+AP^2}}} --> {{{1=1/4+AP^2}}} --> {{{AP^2=1-1/4=3/4}}} --> {{{AP=sqrt(3/4)=sqrt(3)/sqrt(4)=sqrt(3)/2}}}