Question

2sinx - 1 =0. Укажите наибольший отрицательный корень в градусах

Answer 1

Общий вид решения уравнения  sin x  = a, где | a | ≤ 1, определяется формулой:

x = (-1)^k • arcsin(х) +  πk,  k ∈ Z (целые числа).

Так как arcsin(1/2) = π/6, то при к ≥ 0 значение х положительно.

Наибольшее отрицательное значение аргумента будет при к = -1.

Подставим: x = (-1)^(-1) • (π/6) +  π*(-1).

Получим в градусах:  х = -30 - 180 = -210°.

Ответ: наибольший отрицательный корень равен -210 градусов.

Answer 2

Ответ:

-210

Объяснение:

sinx=0,5

x=30+-2π, x=-360+30=-330

x=150+-2π, x=-360+150=-210

Answer 3

To find the largest negative root of the equation 2sin(x) - 1 = 0, we need to solve for x.

Step 1: Add 1 to both sides of the equation: 2sin(x) = 1

Step 2: Divide both sides by 2: sin(x) = 1/2

Step 3: To find the angles where sin(x) = 1/2, we look for the angles where the sine function is positive and equals 1/2. These angles are 30 degrees and 150 degrees in the first and second quadrants, respectively.

Step 4: The largest negative root is in the fourth quadrant. In the fourth quadrant, the sine function is negative. We can use the symmetry of the sine function to find the corresponding angle in the fourth quadrant.

In the fourth quadrant, sin(x) is equal to -1/2 at 210 degrees (180 degrees + 30 degrees).

Thus, the largest negative root of the equation 2sin(x) - 1 = 0 in degrees is x = -210 degrees.