Question

Sin(2x+П/4)=1/2 помогите решить

Answer 1

$\sin(2x+\frac{\pi}{4})=\frac{1}{2}$
$2x+\frac{\pi}{4}=(-1)^k\arcsin(\frac{1}{2})+\pi k, k\inZ$
$2x+\frac{\pi}{4}=\frac{\pi}{6}+\pi k, k\in Z<span>$
$2x=-\frac{\pi}{12}+\pi k, k\in Z<span>$
$x=-\frac{\pi}{24}+\frac{\pi}{2} k, k\in Z<span>$

Answer 2

Problem Statement

The equation to solve is: sin(2x + π/4) = 1/2.

Solution

To solve the equation sin(2x + π/4) = 1/2, we can use trigonometric identities and algebraic manipulation to find the values of x that satisfy the equation.

Let's start by subtracting π/4 from both sides of the equation: 2x + π/4 = arcsin(1/2).

Using the identity sin(arcsin(x)) = x, we can simplify the equation to: 2x + π/4 = π/6.

Now, let's solve for x: 2x = π/6 - π/4.

Simplifying further: 2x = (2π - 3π)/12.

Finally, we can solve for x: x = π/12.

Therefore, the solution to the equation sin(2x + π/4) = 1/2 is x = π/12.

Answer

The solution to the equation sin(2x + π/4) = 1/2 is x = π/12.