Question

Вычислить arcCos(Cos(11 П/8));

Answer 1

$arcCos(Cos(\frac{11\pi }{8}))=arcCos(Cos( \pi +\frac{3\pi }{8}))=arcCos(-Cos\frac{3\pi }{8})=\pi -arcCos(Cos\frac{3\pi }{8})=\pi-\frac{3\pi }{8}=\frac{5\pi}{8}$

Answer 2

To compute arcCos(Cos(11π/8)), we need to find the angle between 0 and π (180 degrees) whose cosine is equal to Cos(11π/8).

It's important to note that the arcCos function returns values in the range [0, π].

To find the angle, we can follow these steps:

1. Reduce the given angle to a range between 0 and 2π (0 and 360 degrees) to make sure it lies within a single period of the cosine function.
2. Use the trigonometric identity: arcCos(Cos(x)) = x if 0 ≤ x ≤ π.
3. If x is outside the range [0, π], we can use the fact that arcCos(Cos(x)) = 2π - x.

Let's proceed with the calculation:

1. Reduce 11π/8 to a range between 0 and 2π: 11π/8 = 8π/8 + 3π/8 = π + 3π/8

2. Check if π ≤ 3π/8 ≤ 2π: Since π is approximately 3.14159 and 2π is approximately 6.28319, we have: π ≤ 3π/8 ≈ 0.98279 ≤ 2π

3. Since 3π/8 is within the range [0, π], we can use the trigonometric identity: arcCos(Cos(3π/8)) = 3π/8

So, arcCos(Cos(11π/8)) ≈ 3π/8.