Question

Cos cos 0.5x=-1 sin sin(4x-п/3)=1/2

Answer 1

Ответ:

Ответ смотри во вложении

Answer 2

To solve the equations:

1. $\cos(0.5x) = -1$
2. $\sin(4x - \pi/3) = 1/2$

Let's solve them one by one:

1. $\cos(0.5x) = -1$

When $\cos(\theta) = -1$, it means that $\theta$ is an odd multiple of $\pi$. So, we have:

$\theta = (2n + 1)\pi$, where $n$ is an integer.

In this case, $\theta = 0.5x$, so:

$0.5x = (2n + 1)\pi$

Now, solve for $x$:

$x = 2(2n + 1)\pi$

2. $\sin(4x - \pi/3) = 1/2$

To solve for $x$, we'll first find the angle whose sine is $1/2$. The angle $\alpha$ that satisfies $\sin(\alpha) = 1/2$ is $\alpha = \pi/6$.

Now, we have:

$4x - \pi/3 = \pi/6 + 2\pi n$ (where $n$ is an integer)

Now, solve for $x$:

$4x = \pi/3 + \pi/6 + 2\pi n$ $4x = 2\pi/3 + 2\pi n$

Divide both sides by 4:

$x = (\pi/3 + 2\pi n)/4$

So, the solutions to the equations are:

1. $x = 2(2n + 1)\pi$ for all integers $n$.
2. $x = (\pi/3 + 2\pi n)/4$ for all integers $n$.