Question

I don’t understand how to use theta (Ø) in trigonometry. I understand what it is, but not how to solve the problems.sin^2(Ø) -4sin(Ø) -5 , where0< (Ø)<360

Answer 1

Given

`\sin^2\theta-4\sin\theta-5,0\leq\theta\leq360\degree`

Find

Solve for x

Step-by-step explanation

given

`\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}`
`\sin\theta=5`

is not possiblre because

`-1\leq\sin\theta\leq1`

so , if

`\begin{gathered} \sin\theta+1=0 \\ \sin\theta=-1 \\ \theta=\sin^(-1)(-1) \\ \theta=(3\pi)/(2) \end{gathered}`

since, general solution is

`\theta=(3\pi)/(2)+2n\pi\lbrace n\in Z\rbrace`

Final Answer

`\theta=(3\pi)/(2)`