Question

Sinx=-1/2 Чему равен х?

Answer 1

ДАНО: sin X = - 0.5

sin 30° = sin π/6 =  +0.5 и sin(-30°) = sin 330° = - 0.5.

Это два значения в пределах оборота. С учетом, что функция периодическая получаем:

х1 = - π/6 + 2*π*n

x2 = 5/6*π + 2*π*n

Answer 2

To find the value of x when sin(x) = -1/2, we need to determine the angle whose sine is -1/2. In which quadrants does the sine function have a value of -1/2?

The sine function is negative in the third and fourth quadrants of the unit circle. In these quadrants, the reference angle whose sine is 1/2 is π/6 radians or 30 degrees.

However, since the sine function is negative in these quadrants, the actual angles will be:

1. In the third quadrant: π + π/6 = 7π/6 radians or 210 degrees.
2. In the fourth quadrant: 2π - π/6 = 11π/6 radians or 330 degrees.

So, there are two possible solutions for x:

1. x = 7π/6 radians (approximately 2.094 radians)
2. x = 11π/6 radians (approximately 5.759 radians)

In degrees, these values are approximately:

1. x ≈ 210 degrees
2. x ≈ 330 degrees