Question

Значение выражения arccos((-V3)/2)+2

Answer 1

$\arccos(-\frac{ \sqrt{3}}{2} )+2= \frac{5\pi}{6} +2$

Answer 2

To find the value of the expression arccos((-√3)/2) + 2, we need to first evaluate the arccosine of (-√3)/2 and then add 2 to the result.

The arccosine function (arccos) gives us the angle whose cosine is equal to the given value. In this case, we want to find the angle whose cosine is (-√3)/2.

The reference angle for arccos((-√3)/2) is π/6 (30 degrees) since the cosine of π/6 is (√3)/2.

However, the given value (-√3)/2 is in the second quadrant of the unit circle, where the cosine is negative. So, the angle whose cosine is (-√3)/2 in the second quadrant is:

π - π/6 = (6π - π)/6 = 5π/6

Now, adding 2 to this angle:

5π/6 + 2 ≈ 5.5236 + 2 ≈ 7.5236

So, the value of the expression arccos((-√3)/2) + 2 is approximately 7.5236 radians. In degrees, it is approximately 430.54°.