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. $\frac{2\pi}{3}$
• B. $\frac{5\pi}{6}$
• C. $\pi$
• D. $\frac{4\pi}{3}$

Hint:

Always check the given range for the angle after finding the trigonometric value to select the correct quadrant.

Answer 1

The Correct Option is B