Question

Sin(arccos(-1/2)) ... Пожалуйста подробнее.

Answer 1

Ответ:V3/2

Пошаговое объяснение:

sin(arccos(-1/2)   arccos(-1/2)=2п/3, т.к. соs2п/3=-1/2 , аsin2п/3=V3/2

Answer 2

To calculate the value of sin(arccos(-1/2)), let's break it down step by step:

1. First, let's find the value of arccos(-1/2). The arccosine (cos^(-1)) function is the inverse of the cosine function. It takes a value between -1 and 1 and returns the angle (in radians) whose cosine is equal to that value.

   arccos(-1/2) = θ cos(θ) = -1/2

2. To find the value of θ, we need to determine in which quadrant the angle lies. Since the cosine is negative, we know that the angle lies in either the second or third quadrant. In these quadrants, the cosine is negative.

3. To further narrow down the possibilities, let's find the reference angle in the first quadrant. The reference angle (ρ) is the acute angle between the terminal side of the angle (θ) and the x-axis.

   cos(ρ) = |cos(θ)| = 1/2 ρ = arccos(1/2) ≈ 60 degrees ≈ π/3 radians

4. Now, we know the reference angle (ρ) is π/3 radians. Since θ lies in either the second or third quadrant, the angle θ can be either: a) π - ρ (second quadrant), or b) 2π - ρ (third quadrant).

   a) θ = π - π/3 = 2π/3 b) θ = 2π - π/3 = 5π/3

5. Next, we'll find sin(θ) for both possible values of θ.

   a) sin(2π/3) sin(2π/3) = sin(120 degrees) ≈ √3/2

   b) sin(5π/3) sin(5π/3) = sin(300 degrees) ≈ -√3/2

So, the two possible values for sin(arccos(-1/2)) are √3/2 and -√3/2, depending on whether the angle θ is in the second or third quadrant.