What is the Value of Sin 90 Degrees ?

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.