Home > Trigonometry > Trigonometric Functions of Any Angle

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)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.