Question

a=arcsin(sin 10)
a=?


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10 radiani, nu grade

Answer 1

a=arcsin(sin10)

1 rad=1*180/π≈57°

10 rad=10*57°=570°

a=arcsin(sin570°)

sin570°=sin(90°*6+30°)=-sin30°=-1/2=-0,5

a=arcsin(-1/2)=-arcsin1/2=-π/6≈ -0,523.

Bafta!

Answer 2

Răspuns:

3π - 10

Explicație pas cu pas:

$\arcsin(\sin x) = \begin{cases} x,\ x\in\Big[-\dfrac{\pi}{2},\dfrac{\pi}{2}\Big]\\ \\ \pi - x,\ x\in \Big[\dfrac{\pi}{2},\dfrac{3\pi}{2}\Big]\\ \\ x-2\pi,\, x\in \Big[\dfrac{3\pi}{2},\dfrac{5\pi}{2}\Big] \\ \\3\pi-x,\x\in \Big[\dfrac{5\pi}{2},\dfrac{7\pi}{2}\Big]\\ \\ \text{si tot asa...}\end{cases}$

$a = \arcsin(\sin 10) \\ \\ 10=x \cdot 3.14 \Rightarrow x = \dfrac{10}{3.14} \approx 3.18\\ \\ \Rightarrow 10 \approx 3.18 \pi \Rightarrow 10\in \Big[\dfrac{5\pi}{2},\dfrac{7\pi}{2}\Big] \\ \\ \Rightarrow \boxed{a = 3\pi - 10 }$