# My infallible calculator

A student came to me today and asked if there was something wrong with my notes because I claimed that $\sin x \ge 0$ for $x \in [2k\pi, (2k+1)\pi]$. The reason that I was wrong was that his calculator told him that $\sin (3\pi) = -1$. 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.

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