Question

What are the trigonometric functions of pi/3?

Answer 1

#{:(sin(pi/3)=sqrt(3)/2,color(white)("XXX"),csc(pi/3)=2/sqrt(3)), (cos(pi/3)=1/2,,sec(pi/3)=2), (tan(pi/3)=sqrt(3),,"cotan"(pi/3)=1/sqrt(3)) :}#

Explanation:

Remembering that an equilateral triangle has all three of its angles equal to `pi/3`,
we can split an equilateral triangle in half as in the image below to obtain the ratios required for the standard trigonometric function definitions.

#{: ("sin"="opposite"/"hypotenuse",color(white)("XXX"),"csc"="hypontenuse"/"opposite"), ("cos"="adjacent"/"hypotenuse",,"sec"="hypotenuse"/"adjacent"), ("tan"="opposite"/"adjacent",,"cotan"="adjacent"/"opposite") :}#