What is the ##sin^(-1)(sqrt(3)/2)##?
February 20th, 2023
##sin^(-1)(sqrt(3)/2) = pi/3## (radians)
##sin^(-1)(sqrt(3)/2) = theta##
##color(white)(“XX”)##means
##sin(theta)=sqrt(3)/2##
##color(white)(“XXXX”)##with the restriction that ##theta in [-pi/2,pi/2]##
The possible triangles with this ratio of ##y## to ##”hypotenuse”## (i.e. ##sin##) are pictured below:
…but note that only ##pi/3## falls within the restricted range for ##sin^(-1)##