Solution :
The value of sin 90 degrees is 1.
Proof :
\(\angle\) A of \(\Delta\) ABC is made large and large until it becomes 90 degrees. As \(\angle\) A gets large and large \(\angle\) C gets smaller and smaller. Side AB goes on decreasing. The point A gets closer to point B. When \(\angle\) C becomes very close to 0 degree. The side AC almost coincide with side BC and side AB becomes to zero.
So, AC = BC and AB = 0
By using trigonometric formulas,
\(sin 90^{\circ}\) = \(perpendicular\over hypotenuse\) = \(p\over h\)
\(sin 90^{\circ}\) = \(BC\over AC\) = \(BC\over BC\) = 1
Hence, the value of \(sin 90^{\circ}\) = 1.
