Question

How do you evaluate `sin (pi/2)`?

Answer 1

If in a right angled triangle `theta` represents one of its acute angle then by definition we can write

`color(red)(sintheta="Opposite"/"Hypotenuse")`

Now if we increase the magnitude of `theta` slowly then the magnitude of opposite will slowly go to increase and the magnitude of adjacent will go to decrease. When `theta` becomes equal to `pi/2` then adjacent will vanish and opposite will coincide with the hypotenuse.

This means when #theta=pi/2" then #"opposite"="hypotenuse"#

So then

`color(blue)(sintheta="Opposite"/"Hypotenuse")`

`=>color(blue)(sin(pi/2)=cancel"Hypotenuse"/cancel"Hypotenuse"=1)`