Hi, I was wondering if you could explain to me how x + y= π/2, sin x = cos y. Thank you!

To understand this rule (which obviously works in degrees just as it does in radians), turn to right triangles.

Below, you’ve got a right triangle with acute angles measuring *x*° and *y*°. Because the third angle in the triangle is a right angle, and because the angles in *any* triangle add up to 180°, we know that no matter what *x* and *y* are,

*x°* + *y°* = 90°.

So far so good?

Now let’s list out some trigonometric ratios using out old pal SOH-CAH-TOA (well, really just the SOH and CAH parts for this demonstration).

There you have it. and , just by nature of *x*° and *y*° being the measures of the two acute angles in the same right triangle.

The trick is, for *any* two angles that add up to 90°, you can draw a right triangle that contains them. Therefore, for any two angles that add up to 90° (or *π*/2 radians) *x* and *y*, sin *x* = cos *y* and sin *y* = cos *x*.