1.Вычислите: arccos(cos13) 2, Найдите Область Определения Функции: y=1/3arcsin4x. Created by Nastenka7878. algebra-ru

3arcsin4x...

Nastenka7878 @Nastenka7878

July 2022 2 13 Report

1.Вычислите:
arccos(cos13)
2, Найдите Область Определения Функции:
y=1/3arcsin4x

Rechnung

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Arccos(cos 13)=13

y=1/3*arcsin(4x)
D(arcsinx)=[-1;1]
D(arcsin(4x))=[-1;1]
D(1/3*arcsin(4x))=[-1/3;1/3]

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nafanya2014

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1)По определению
0 ≤ arccos a ≤ π
-1 ≤ a ≤ 1
и   arccos(cos α)= α, если 0 ≤ α ≤ π

cos(13)=cos(4π-13)    и угол (4π-13) находится в первой четверти, т.е
0 ≤ (4π-13) ≤ π
Поэтому arccos(cos 13)=arccos(cos (4π-13))=4π-13

2) D(arcsin t)=[-1;1]
   -1 ≤ 4x ≤ 1
   -1/4 ≤ x ≤ 1/4
Ответ. [-1/4; 1/4]

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