What are the trigonometric functions of pi/3?

1 Answer
Alan P.
Jul 25, 2016

#{:(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.

enter image source here

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

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