Question

Sin(x/2)=0,5 ришить бистпро

Answer 1

$\sin( \frac{x}{2} ) = 0.5 \\ \sin( \frac{x}{2} ) = \frac{1}{2} \\ \frac{x}{2} = ( - 1)^{n} \arcsin( \frac{1}{2} ) + \pi n \\ x = ( - 1)^{n} \frac{2\pi}{6} + 2\pi n \\ x = ( - 1)^{n} \frac{\pi}{3} + 2\pi n, \: n \in Z$

Answer 2

To solve the equation sin(x/2) = 0.5, we can use basic trigonometric identities and algebraic manipulation. The goal is to find all possible values of x that satisfy the equation.

Step 1: Convert 0.5 to its corresponding trigonometric value. sin(30°) = 0.5

Step 2: Apply the double-angle formula for sine. sin(x/2) = sin(30°) sin(x/2) = sin(π/6)

Step 3: Set the angle x/2 equal to π/6 and find the general solutions. x/2 = π/6 + 2πn or x/2 = π - π/6 + 2πn

where n is an integer (positive, negative, or zero) that represents multiple solutions.

Step 4: Solve for x. For x/2 = π/6 + 2πn: x = π/3 + 4πn

For x/2 = π - π/6 + 2πn: x = 5π/3 + 4πn

So the general solutions for x are: x = π/3 + 4πn, 5π/3 + 4πn

where n is an integer. These solutions cover all possible values of x that satisfy the equation sin(x/2) = 0.5.