Use linearisation to estimate sin(0.1). (Use sin(0) = 0 and cos(0) = 1.) Set the slider to your answer.

0.1 (answers within ±0.01 count)

$L(x) = \sin(0) + \cos(0)\cdot(x - 0) = x$. So $\sin(0.1) \approx 0.1$ (actual value $\approx 0.0998$).