Question

Sin x = 0,6; X€(2pi/2; pi); tg x?

Answer 1

Ответ:

Для решения этой задачи нам нужно использовать тригонометрические соотношения.

Для начала найдем значение cos(x), так как у нас есть значение sin(x):

sin(x) = 0,6

cos(x) = ±√(1 - sin²(x)) = ±√(1 - 0,6²) = ±0,8

Так как x находится во втором и третьем квадрантах (2π/2 < x < π), то cos(x) < 0. Значит, cos(x) = -0,8.

Теперь мы можем найти значение tg(x):

tg(x) = sin(x) / cos(x) = 0,6 / (-0,8) = -0,75

Ответ: tg(x) = -0,75.

Answer 2

To find the value of the tangent (tan) of x when sin(x) = 0.6 and x is in the interval (2π/2, π), you can use the following steps:

1. First, identify the angle whose sine is 0.6 within the specified interval. Since sin(x) = 0.6, you can use the inverse sine function (arcsin or sin^(-1)) to find the angle:

   x = arcsin(0.6)

2. Calculate the value of x using a calculator:

   x ≈ 0.6435 radians

3. Now that you have the value of x, you can find the tangent of x:

   tan(x) = tan(0.6435)

4. Calculate the tangent using a calculator:

   tan(x) ≈ 0.7482

So, the tangent of x, where x is approximately 0.6435 radians and x is in the interval (2π/2, π), is approximately 0.7482.