Question

Вычислите: arccos (-√3/2) +arctg(-√3)

Answer 1

Ответ:

$\frac{5\pi}{6} - \frac{\pi}{3} \\ \frac{5\pi - 2\pi}{6} \\ \frac{3\pi}{6} \\ \frac{\pi}{2}$

Answer 2

To compute the value of the expression, we need to find the arccosine of (-√3/2) and the arctangent of (-√3) separately, and then add them together.

1. arccos(-√3/2): The arccosine function (arccos) gives us the angle whose cosine is a given value. So, we need to find the angle whose cosine is (-√3/2).

The cosine of π/6 radians is √3/2, so: arccos(-√3/2) = π - π/6 = 5π/6

2. arctg(-√3): The arctangent function (arctg or atan) gives us the angle whose tangent is a given value. So, we need to find the angle whose tangent is (-√3).

The tangent of -π/3 radians is -√3, so: arctg(-√3) = -π/3

Now, we add the results together: arccos(-√3/2) + arctg(-√3) = 5π/6 + (-π/3)

To add these fractions, we need a common denominator, which is 6. So, we convert -π/3 to -2π/6:

5π/6 + (-π/3) = 5π/6 - 2π/6 = (5π - 2π) / 6 = 3π / 6 = π / 2

So, the value of the expression is π / 2, which is approximately 1.5708 radians or 90 degrees.