Let \(B_t\)  be a standard Brownian motion. For each of the following definitions of  \(Y_t\), find adapted stochastic process \(\mu_t\) and \(\sigma_t\) so that \(dY_t =\mu_t dt + \sigma_t dB_t\)

1. \( Y_t =\sin(B_t) \)
2. \( Y_t= (B_t)^p \) for \(p>0\)
3. \( Y_t=\exp( B_t – t^2)\)
4. \(Y_t=\log(B_t) \)
5. \(Y_t= t^2 B_t \)