Question

Solve the equation for 0

Answer 1

The answerGiven the equation

`-2+\sin \theta=\frac{-4+\sqrt[]{2}}{2}`

Step 1: Collect like terms

`\sin \theta=\frac{-4+\sqrt[]{2}}{2}+2`
`\sin \theta=\frac{-4+\sqrt[]{2\text{ }}+4}{2}`
`\sin \theta=\frac{\sqrt[]{2}}{2}`

Step 2: Find the value of the angle

`\theta=\sin ^(-1)(\frac{\sqrt[]{2}}{2})`

`\begin{gathered} \text{for the range of }\theta\text{ given } \\ 0\leqslant\theta\leqslant2\pi \end{gathered}`
`\theta=45^0,135^0`

Then is expressing in radians

`\begin{gathered} 45^0=(\pi)/(4) \\ 135^0=(3\pi)/(4) \end{gathered}`

Answer is option B