Question

Cos(arccos0,2)+arccos(cos2π5)+arccos(−3√2)

Answer 1

Не имеет смысла, поскольку arccos определен в интервале [-1.1] и аргумент по модулю не может быть >1, а |-3$\sqrt{2}$| > 1

Пошаговое объяснение:

Answer 2

To evaluate the expression cos(arccos(0.2)) + arccos(cos(2π/5)) + arccos(-3√2), we'll break it down step by step:

1. cos(arccos(0.2)): The inner expression arccos(0.2) gives us an angle whose cosine is 0.2. Let's denote this angle as θ. Therefore, θ = arccos(0.2).

   Now, we can evaluate cos(θ) to find the value of cos(arccos(0.2)). cos(arccos(0.2)) = cos(θ) = 0.2.

2. arccos(cos(2π/5)): The inner expression cos(2π/5) gives us the cosine of the angle 2π/5. We'll denote this angle as φ.

   Now, we can evaluate arccos(cos(2π/5)) to find the value of φ. Since the arccosine and cosine functions are inverses of each other, arccos(cos(2π/5)) = 2π/5.

3. arccos(-3√2): We have arccos(-3√2), which means we need to find the angle whose cosine is -3√2. Let's denote this angle as ψ.

   Now, we can evaluate arccos(-3√2) to find the value of ψ. Since the cosine function is positive in the second and third quadrants, we can find the reference angle: reference angle = arccos(3√2)

   However, since we have a negative sign, the angle ψ will be in the second quadrant (180° < ψ < 270°). Therefore, ψ = 180° - reference angle.

   Using a calculator or approximating the value, we get: arccos(-3√2) ≈ 180° - 55.51° ≈ 124.49°.

Now, we can substitute the values we found into the expression: cos(arccos(0.2)) + arccos(cos(2π/5)) + arccos(-3√2) = 0.2 + 2π/5 + 124.49°

Note: In trigonometric calculations, angles are often measured in radians. If you prefer to use radians instead of degrees, you can convert the degrees to radians using the conversion factor: 1° = π/180 radians.