Question

Solve 2sin (2x) + 2 = 0 on the interval [0, 27).π 3π 9π 11π8' 85π 7π4 4π 9π8' 85π 7π 13π 15π8' 8' 8' 8

Answer 1

`\begin{gathered} 2\sin \mleft(2x\mright)+√(2)=0 \\ 2\sin \mleft(2x\mright)=-√(2) \\ \sin \mleft(2x\mright)=-(√(2))/(2) \\ \text{General solution for }\sin \mleft(2x\mright)=-(√(2))/(2) \\ 2x=(5\pi)/(4)+2\pi n,\: 2x=(7\pi)/(4)+2\pi n \\ x=(5\pi)/(8)+\pi n,\: x=(7\pi)/(8)+\pi n \end{gathered}`