JUST sold out . Wow <| sep |> Logically it follows that if you take the sine and cosine of the same angle and add them you will always get 1 sine and cosine can be thought of as the percentage that the vertical and horizontal components respectively contribute to the vector of interest , 1 being 100 %, which is why sin 90 , a vertical line , is 1 , while the cosine of the same angle is 0 . This is why sin 45 cos 45 12 , both the vertical and horizontal components contribute equally to the vector pointing at a 45 degree angle . Wait , what ? ?? You seem to generally know what you ' re talking about , so I don ' t know if I ' m misreading you , if there ' s some kind of typo , or what . But sin 45 cos 45 1 sqrt 2 , not 12 , and sinxcosx is not 1 , but rather a wave with a peak of sqrt 2 at 45 degrees .