Respuesta :
Given
[tex]\sin^2\theta-4\sin\theta-5,0\leq\theta\leq360\degree[/tex]Find
Solve for x
Explanation
given
[tex]\begin{gathered} \sin^2\theta-4\sin\theta-5=0 \\ \sin^2\theta-5\sin\theta+\sin\theta-5=0 \\ \sin\theta(\sin\theta-5)+1(\sin\theta-5)=0 \\ (\sin\theta+1)(\sin\theta-5)=0 \\ so,either \\ (\sin\theta+1)=0,or \\ (\sin\theta-5)=0 \end{gathered}[/tex][tex]\sin\theta=5[/tex]is not possiblre because
[tex]-1\leq\sin\theta\leq1[/tex]so , if
[tex]\begin{gathered} \sin\theta+1=0 \\ \sin\theta=-1 \\ \theta=\sin^{-1}(-1) \\ \theta=\frac{3\pi}{2} \end{gathered}[/tex]since, general solution is
[tex]\theta=\frac{3\pi}{2}+2n\pi\lbrace n\in Z\rbrace[/tex]
Final Answer
[tex]\theta=\frac{3\pi}{2}[/tex]