How do you evaluate sin(π/4)?

1 Answer
Feb 11, 2016

#sqrt(2)/2#

Explanation:

In the trigonometric circle #pi/4# is the bisectrix between 0 and #pi/2#, where x=y.
By the Pythogoras theorem we know that #x^2+y^2=1#.

If you don't know the trigonometric circle, you can see that if one of the small angles of a rectangle triangle is #pi/4#, the other will be also #pi/4#, which implies the catets are equal.

So if x=y, you will have

#x^2+y^2=1#

#2y^2=1#

#y^2=1/2#

#y=sqrt(1/2)=sqrt(2)/2#

To get the sin of #pi/4# you divide the opposite catet (#sqrt(2)/2#)
by the hypothenuse( 1).

You'll get #sqrt(2)/2#