Question

Sin ([3pi over 2] + x) + sin ([3pi over 2] + x) = -2must show work also

Answer 1

`x=0\text{\degree}+360\text{\degree{}n}`

Explanation:

We have the following equation:

`sin\: \mleft(\mleft[(3\pi)/(2)\mright]+x\mright)\: +\: sin\: \mleft(\mleft[(3\pi\:)/(2)\mright]+x\mright)\: =\: -2`

Solving for x:

`\begin{gathered} 2\cdot sin\: (\lbrack(3\pi)/(2)\rbrack\: +\: x)\: \: =\: -2 \\ sin\: (\lbrack(3\pi)/(2)\rbrack\: +\: x)=-(2)/(2) \\ sin\: (\lbrack(3\pi)/(2)\rbrack\: +\: x)=-1 \\ (3\pi)/(2)+\: x=\arcsin (-1) \\ (3\pi)/(2)+\: x=(3\pi)/(2)+\: 2\pi n \\ x=2\pi n \\ x=0\text{\degree}+360\text{\degree{}n} \\ \text{for n = 0} \\ \end{gathered}`