Задача 61861 Y : - T arcty FRrcos(~ 2 Е et = .,\,} ::...

6196a43161acd962013bfaf4

29.11.2021 12:25:53

Y : - T arcty FRrcos(~ 2 Е et = .,\,} :: К . В р : p i k- e B b p:

5f3ea7e3faf909182968ddd9

29.11.2021 12:38:15

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[m]arcsin\frac{\sqrt{2}}{2}=\frac{π}{4}[/m], так как [m]sin\frac{π}{4}=\frac{\sqrt{2}}{2}[/m] и [m]\frac{π}{4} ∈ [-\frac{π}{2};\frac{π}{2}][/m]

[m]arctg(-1)=-\frac{π}{4}[/m], так как [m]tg(-\frac{π}{4})=-1[/m] и [m]-\frac{π}{4} ∈ [-\frac{π}{2};\frac{π}{2}][/m]

[m]arccos(-\frac{\sqrt{3}}{2})=π- arccos\frac{\sqrt{3}}{2}=π-\frac{π}{3}=\frac{2π}{3}[/m], так как [m]cos\frac{2π}{3}=-\frac{\sqrt{3}}{2}[/m] и [m]\frac{2π}{3} ∈ [0;π][/m]


[m]arcsin\frac{\sqrt{2}}{2}-4arctg(-1)+arccos(-\frac{\sqrt{3}}{2})=\frac{π}{4}-4\cdot \frac{π}{4}+ \frac{2π}{3}=-\frac{π}{12}[/m]