If, for the matrix , , then the number of possible values of in…

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

If, for the matrix A=[cos⁡θ2sin⁡θsin⁡θcos⁡θ]A=\begin{bmatrix}\cos\theta&2\sin\theta\\\sin\theta&\cos\theta\end{bmatrix}, A−1=ATA^{-1}=A^T, then the number of possible values of θ\theta in [0,2π][0,2\pi] is: (a) 22 (b) 33 (c) 11 (d) 44

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