What is the #sin^(-1)(sqrt(3)/2)#?
The possible triangles with this ratio of
...but note that only
It helps if one recognises the lengths 3 and
being two of the sides in one of the special triangle,
namely 30°, 60° 90°.
Sketch this by drawing an equilateral triangle of sides 2 units, and drawing in a line of symmetry to form two right-angled triangles.
The hypotenuse is of length 2 units and the opposite side
is of length
However, the sign is positive. Sin is positive in the first and second quadrants.