ответ: 
Решение.
![=\Big[\ \dfrac{13\pi }{16}=146,25^\circ\in (90^\circ ;180^\circ )\notin (-\90^\circ ;90^\circ )\Big]=\\\\=arcsin\Big(sin\Big(\pi -\dfrac{3\pi }{16}\Big)\Big)=arcsin\Big(sin\dfrac{3\pi }{16}\Big)=\Big[\ \dfrac{3\pi }{16}=33,75^\circ \in (-90^\circ ;90^\circ )\ \Big]=\\\\=\dfrac{3\pi }{16}](/tpl/images/1357/6277/1cc61.png)
Вычислить arcsin(sin(141π/16)
ответ: 3π/16 .
Объяснение: - π/2 ≤ arcsin(a) ≤ π/2
sin141π/16 =sin(9π- 3π/16 )= sin(3π/16) .
* * * 3π/16=(π/2)*(3/8) < π/2 * * *
arcsin(sin(141π/16) =arcsin(sin(3 π/16) =3π/16.
sin(141π/16) =sin(8π+ 13π/16)= sin(13π/16)= sin(π -3π/16) =sin(3π/16) .
