Question

Cos6x=-9/8 решение уравнения

Answer 1

Cos6x = - 9/8
Так как - 9/8 = - 1,125 и - 1,125 ∉ [ - 1; 1]
то данное уравнение решений не имеет

Answer 2

Ответ: уравнение не имеет решений .

Пошаговое объяснение:

       $cos\, 6x=-\frac{9}{8}$

Так как   $-1\leq cos\, 6x\leq 1$  , а число  $-\frac{9}{8}$  , то   $cos\, 6x$ не может принимать значение, равное  $-\frac{9}{8}$  , меньшее -1. Поэтому уравнение не имеет решений.

Answer 3

To solve the equation cos(6x) = -9/8, we need to find the values of x that satisfy the equation. Let's break down the solution step by step:

1. Start by finding the inverse cosine of both sides of the equation to isolate x: cos^(-1)(cos(6x)) = cos^(-1)(-9/8).

2. Simplify the left side using the identity cos^(-1)(cos(x)) = x, where x is in the range of the inverse cosine function: 6x = cos^(-1)(-9/8).

3. Now, we need to find the principal value of cos^(-1)(-9/8). However, the range of the inverse cosine function is [0, π], so we need to adjust the equation accordingly.

4. First, find the principal value of cos^(-1)(9/8): cos^(-1)(9/8) ≈ 0.7227 radians (principal value in the range [0, π]).

5. Since cosine is an even function, we have cos^(-1)(-9/8) = -cos^(-1)(9/8) ≈ -0.7227 radians.

6. Substitute this value back into the equation: 6x ≈ -0.7227.

7. Finally, solve for x: x ≈ -0.7227/6 ≈ -0.1205 radians (approximately).

Therefore, one solution to the equation cos(6x) = -9/8 is x ≈ -0.1205 radians.