Why sin90 equals 1 when practically no triangle is formed at angle of 90 degrees?

Answer 1

Sine is a function which is defined for all real numbers: so you can have sin(240 degrees) which, given that a triangle cannot have any angle of 240 deg) appears to make no sense at all. This is because you are limiting the sine function by its definition in the context of a right angled triangle.

There are at least two other ways of defining the sine function. One of them is to consider a unit circle at the origin. That is, a circle with centre at (0,0) and radius = 1. Measure the angle, x, between the radius and the x-axis in the anti-clockwise direction. Then sin(x) is the y-coordinate of the point where the radius reaches the circle or, the vertical height of that point..

Another way to define sine is as the following infinite sum:

sin(x) = x - x^3/3! + x^5/5! + x^7/7! - ... where x is any angle measured in radians. (If you need to convert then 180 degrees = pi radians).

Answer 2

Sin is Opposite/Hypotenuse. Think of the right angle in a triangle: the Opp and Hyp are the same side so sin 90 is 1.