Question

Sin x/6=-1 решите пжл))

Answer 1

X/6 = -п/2+2пn, n принадлежит Z

x=- 6п/2 +12пn, n принадлежитZ

x=-3п +12пn, n принадлежитZ

Answer 2

To solve the equation sin(x/6) = -1, we need to find the values of x that satisfy this equation.

First, let's recall the unit circle definition of the sine function. For any angle θ, sin(θ) represents the y-coordinate of the point on the unit circle corresponding to that angle.

Since sin(x/6) = -1, we need to find the angles x/6 for which the y-coordinate is -1. On the unit circle, the angle whose y-coordinate is -1 is π/2 radians (or 90 degrees). This means x/6 must be an angle whose sine is π/2.

Using the inverse sine function (also known as arcsine or sin^(-1)), we can find the solution:

x/6 = arcsin(-1)

The arcsine function returns an angle between -π/2 and π/2, so the solution for x/6 will be in that range.

The angle whose sine is -1 is -π/2, so we have:

x/6 = -π/2

To solve for x, we multiply both sides of the equation by 6:

x = -π/2 * 6

x = -3π

Therefore, the solution to the equation sin(x/6) = -1 is x = -3π (or -3 times pi).

Please note that this is one of the possible solutions, and there are infinitely many values of x that satisfy the equation sin(x/6) = -1, differing by multiples of 2π.