Question

Cos[4x+pi/8]=0 Help pls

Answer 1

Ответ:

$\cos(4x + \frac{\pi}{8} ) = 0 \\ 4x + \frac{\pi}{8} = \frac{\pi}{2} + \pi \: n \\ 4x = \frac{3\pi}{8} + \pi \: n \\ x = \frac{3\pi}{32} + \frac{\pi \: n}{4}$

n принадлежит Z.

Answer 2

To solve the trigonometric equation $\cos(4x + \frac{\pi}{8}) = 0$, you can follow these steps:

1. Use the fact that $\cos(\theta) = 0$ when $\theta$ is an odd multiple of $\frac{\pi}{2}$. So, set $4x + \frac{\pi}{8}$ equal to an odd multiple of $\frac{\pi}{2}$:

   $4x + \frac{\pi}{8} = (2n + 1)\frac{\pi}{2}$, where $n$ is an integer.

2. Solve for $x$ by isolating it on one side of the equation:

   $4x = (2n + 1)\frac{\pi}{2} - \frac{\pi}{8}$

3. Divide both sides by 4 to solve for $x$:

   $x = \frac{(2n + 1)\frac{\pi}{2} - \frac{\pi}{8}}{4}$

Now, you have the general solution for $x$, which includes all possible values that satisfy the equation. $n$ can be any integer, so this equation represents an infinite set of solutions.

To find specific solutions, you can plug in different integer values for $n$. Each value of $n$ will give you a unique solution for $x$.