Question

Arcsin2x=0 математика​

Answer 1

Ответ:

0

Пошаговое объяснение:

arcsin 2x = 0, значит sin 0 = 2x и 2x принадлежит [-pi/2; pi/2]

В нашем случае получаем 2x = 0, x = 0 - принадлежит указанному промежутку!

Answer 2

To solve the equation arcsin(2x) = 0, we can rewrite it in terms of the inverse trigonometric function sine.

The arcsin function is the inverse of the sine function, so arcsin(sin(x)) = x for certain values of x.

In this case, arcsin(2x) = 0 can be written as sin(arcsin(2x)) = sin(0).

Since sin(0) = 0, we have sin(arcsin(2x)) = 0.

Therefore, arcsin(2x) = 0 implies 2x = sin⁻¹(0).

The sine function is equal to zero at multiples of π, so sin⁻¹(0) = nπ, where n is an integer.

Thus, 2x = nπ.

Finally, we solve for x by dividing both sides by 2:

x = nπ/2.

Therefore, the solution to the equation arcsin(2x) = 0 is x = nπ/2, where n is an integer.