# What is the #sin^(-1)(sqrt(3)/2)#?

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The possible triangles with this ratio of

...but note that only

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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.

Therefore

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