Let [A = ( pmatrix & - & pmatrix )], ([ ] [ ] R) such that [A^32 = ( pmatrix 0 & - 1 1 & 0…

Question

Let $$A = \left( {\begin{pmatrix} {\cos \alpha } & { - \sin \alpha }  \
   {\sin \alpha } & {\cos \alpha }  \ \end{pmatrix} } \right)$$, ($$\alpha $$ $$ \in $$ R)
 such that $${A^{32}} = \left( {\begin{pmatrix} 0 & { - 1}  \
   1 & 0  \ \end{pmatrix} } \right)$$ then a value of $$\alpha $$ is

Accepted Answer

From here sin 32$$\alpha $$ = 1 and cos 32$$\alpha $$ = 0

$$ \therefore $$ 32$$\alpha $$ = 2n$$\pi $$ + $${\pi  \over 2}$$

$$ \Rightarrow $$ $$\alpha $$ = $${\pi  \over {64}} + {{n\pi } \over {16}}$$

Putting n = 0, $$\alpha $$ = $${\pi  \over {64}}$$

Solutions · 1