Question

How do you evaluate sin(π/4)?

Answer 1

`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`