(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have

[tex]

J=\begin{bmatrix}

\frac{\pi}{2}&0&0\\

1&\frac{\pi}{2}&0\\

0&1&\frac{\pi}{2}\\

\end{bmatrix}

[/tex]

I need to find [tex] \sin(J) \text{ and } \cos(J) \text{ and show that } \sin^{2}(J)+\cos^{2}(J)=I

[/tex]

2. Relevant equations

3. The attempt at a solution

I have the following:

[tex]

\sin(J)=

\begin{bmatrix}

1&0&0\\

0&1&0\\

0&0&1\\

\end{bmatrix}

[/tex]

and

[tex]

\cos(J)=

\begin{bmatrix}

0 & 0 & 0\\

0 & 0 & 0\\

0 & 0 & 0\\

\end{bmatrix}

[/tex]

I don't know if this is correct. All the questions I have examples of have more than one eigenvalue, this one only has one eigenvalue.

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# Homework Help: Spectral decomposition of a diagonal matrix

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