I typed the derivative of $\sin(x)$ at $x=0$ into my calculator, and it outputted $0.0174...$ I was expecting the answer $1$. What went wrong?
2026-03-26 11:18:19.1774523899
Why does the TI-30X Pro calculator seem to get the derivative of $\sin(x)$ at $x=0$ wrong?
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Your calculator is in degrees mode. As such, it is calculating the derivative of the function $\sin (x^\circ)$, which is $\dfrac{2\pi}{360}\cos(x^\circ)$. At $x=0$, we have $\dfrac{2\pi}{360}\cos(x^\circ)=\dfrac{2\pi}{360}\cos 0=\dfrac{2\pi}{360}$, which agrees with the result given on the calculator.
By contrast, the derivative of the function $\sin x$ is $\cos x$, and $\cos0=1$. Therefore, if your calculator is set to radians mode, it ought to output $1$.