Question

If $A = \begin{bmatrix} \sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha \end{bmatrix}$ and $\alpha \in (\frac{\pi}{2}, \frac{3\pi}{2})$, if $A + A^T = I$, then $\alpha =$}

• A. $2\pi/3$
• B. $5\pi/6$
• C. $\pi$
• D. $4\pi/3$

Hint:

$\sin \theta = 1/2$ has two solutions in $(0, 2\pi)$. Use the interval $(\pi/2, 3\pi/2)$ to choose the correct one.

Answer 1

The Correct Option is B