Question

Solve each of the following. Please give both the general solution and the specific solutions in the given interval.
1. 2sin(2theta)+√3=0 interval [0,2π)

Answer 1

\[2\sin2 \theta+\sqrt{3}=0\]

Answer 2

\[\sin2\theta=-\sqrt{3/4}\]

Answer 3

\[2\sin(2\theta)+√3=0 \rightarrow 2\sin(2\theta)=-√3 \rightarrow \sin(2\theta)=-√3/2\
\[\sin(2\theta)=-√3/2 \rightarrow \sin(2\theta)=- \sin \frac{\pi}{3} =\sin (\pi+\frac{\pi}{3})\]
\[ \sin(2\theta)= =\sin (\frac{4\pi}{3}) \rightarrow 2\theta =\frac{4\pi}{3} \rightarrow \theta = \frac{4\pi}{3 \times 2}\]
\[\rightarrow \theta = \frac{2\pi}{3 }\]

Answer 4

@yueyue

Answer 5

@dpasingh Alright thank you but do you have any idea what it means when it mentions the general solution and the specific solutions?