Question

Решить уравнение sinx=-1​

Answer 1

Частный случай

х=3П/2+2Пн

Answer 2

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

In the unit circle, the sine function takes on its maximum value of 1 at π/2 (90 degrees) and its minimum value of -1 at -π/2 (-90 degrees). Since we are looking for sin(x) = -1, we want to find the angles where the sine function equals -1.

The angle -π/2 (-90 degrees) and 3π/2 (270 degrees) have a sine of -1. Additionally, any angle that is coterminal to these angles (i.e., can be obtained by adding or subtracting multiples of 2π) will also have a sine of -1.

So, the solutions to the equation sin(x) = -1 are: x = -π/2 + 2πn, where n is an integer.

For example, when n = 0, x = -π/2 + 2π(0) = -π/2 and when n = 1, x = -π/2 + 2π(1) = 3π/2.

Keep in mind that there are infinitely many solutions, as there are an infinite number of integers for n. The solutions are all the angles that have a sine of -1, which repeat every 2π radians (360 degrees).