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

$\begin{gathered} 45^0=\frac{\pi}{4} \\ 135^0=\frac{3\pi}{4} \end{gathered}$

Answer is option B