Why is the sine of 90 degrees 1?

So, Why Exactly is the Sine of 90 Degrees Equal to 1?

The sine function. You probably remember it from high school trigonometry, right? It’s this cool way of relating angles in a right triangle to the ratio of its sides. Basically, for any angle in that triangle, the sine is just the length of the side opposite the angle divided by the hypotenuse. Simple enough, right? But then comes the head-scratcher: how does that explain why the sine of 90 degrees is exactly 1? Let’s break it down.

The Right Triangle Trick

Okay, picture this: a right triangle. Now, imagine one of the pointy angles getting bigger and bigger, creeping closer and closer to 90 degrees. What happens? Well, the side opposite that angle starts to stretch out, almost becoming the same length as the longest side, the hypotenuse. Now, here’s the kicker: if that angle actually hits 90 degrees, the opposite side and the hypotenuse basically become one and the same. They overlap completely!

Think about it: