My infallible calculator

A student came to me today and asked if there was something wrong with my notes because I claimed that [tex] \sin x \ge 0[/tex] for [tex] x \in [2k\pi, (2k+1)\pi] [/tex]. The reason that I was wrong was that his calculator told him that [tex] \sin (3\pi) = -1 [/tex]. I tried to convince him to use his knowledge of trigonometry that the value was 0 to no avail. I then asked him to check his calculator and waited for him to pull it out of his bag and input the value — it took perhaps a minute but it felt much longer — and finally he was convinced.