Question

Question #03cdf

Answer 1

Take an equilateral triangle with sides , say a, and draw a perpendicular to the base from opposite vertex. The angles of each of the triangles are 30,60, 90 with sides a, a/2 and
(`sqrt3`/2)a

Explanation:

Now cos 30 = {(`sqrt3`/2)a}/a = `sqrt`3/2
sin 30 = (a/2)/a = 1/2 etc.
sin 60 = cos 30 = `sqrt`3/2 etc
For trigonometric functions of 90, we consider a unit circle and proceed.
Note : too long a quest to give a comprehensive answer