3. Яка з наведених рівностей е пропорцією? a)39/19=60/3; 6)1/4₁=3:4; B)48/16=24/6; r) 50:5=20:4.​

Certainly! Let's solve the equation \( \sin(2x) = -1 \) step by step.

1. **Initial Equation:**
\[ \sin(2x) = -1 \]

2. **Apply Inverse Sine Function:**
\[ 2x = \arcsin(-1) \]

The inverse sine function of -1 is \(-\frac{\pi}{2}\). Therefore,
\[ 2x = -\frac{\pi}{2} \]

3. **Solve for x:**
Divide both sides by 2:
\[ x = -\frac{\pi}{4} \]

So, the solution to the equation \( \sin(2x) = -1 \) is \( x = -\frac{\pi}{4} \).