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 \(dY_t =\mu_t dt + \sigma_t dB_t\)

- \( Y_t =\sin(B_t) \)
- \( Y_t= (B_t)^p \) for \(p>0\)
- \( Y_t=\exp( B_t – t^2)\)
- \(Y_t=\log(B_t) \)
- \(Y_t= t^2 B_t \)