Answer
(a) $\omega = 175~rad/s$
(b) The instantaneous value of the emf is $~~-10.4~V$
Work Step by Step
(a) The phasor rotates counterclockwise through an angle of $\theta = \frac{5\pi}{6}~rad$ in a time of $15~ms$
We can find the angular frequency $\omega$:
$\omega~t = \theta$
$\omega = \frac{\theta}{t}$
$\omega = \frac{\frac{5\pi}{6}~rad}{15\times 10^{-3}~s}$
$\omega = 175~rad/s$
(b) The instantaneous value of the emf is the horizontal component of the phasor:
$(12~V)~(cos~\frac{5\pi}{6}) = -10.4~V$
The instantaneous value of the emf is $~~-10.4~V$
