How do you evaluate sin (pi/2)?

1 Answer
P dilip_k
Aug 15, 2016

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)

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