Question

Решите уравнение sin x/4=1​

Answer 1

x/4=a

sina=1

a=pi/2+2pi*n, n∈Z.

x=2pi+8pi*n, n∈Z.

Ответ: x=2pi+8pi*n, n∈Z.

Answer 2

To solve the equation sin(x/4) = 1, we need to find the values of x that satisfy the equation.

The sine function takes values between -1 and 1, and when sin(x/4) = 1, it means that x/4 is equal to the sine inverse of 1, which is π/2.

So, we have:

x/4 = π/2

To find the values of x, we can multiply both sides by 4:

x = 4 * (π/2)

x = 2π

But keep in mind that the sine function is periodic, and it repeats every 2π. So, there are infinitely many solutions to this equation. The general solution is given by:

x = 2π + 2πk

where k is an integer (positive, negative, or zero) representing the number of complete sine cycles.

So, the solutions for x are all values of the form:

x = 2π, 4π, 6π, ..., 2πk, ...

where k is an integer.