Let

$$A(t) = \left\lbrack \begin{array}{rr} 3\sin\!\left(t\right) & -4\cos\!\left(t\right) \\ 3\sin\!\left(t\right) & 4\cos\!\left(t\right) \end{array} \right\rbrack.$$

1. Find the values of $t$ such that $A(t)$ is not invertible. You may use $k$ to denote any possible integer in your answer (e.g., if the answer is all integer multiples of $5$, you would enter $5k$, where $k$ is any integer).
   
   $A(t)$ is not invertible when $t =$ , where $k$ is any integer.
   
   
2. Find a formula for $A^{-1}(t)$ for the values of $t$ for which $A(t)$ is invertible.

   $A^{-1}(t) =$

   $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$