A circular coil with a diameter of 22.0 cm and 155 turns rotates about a vertical axis with an angular speed of 1250 rpm. The only magnetic field in this system is that of the Earth. At the location of the coil, the horizontal component of the magnetic field is 3.80 * 10-5 T, and the vertical component is 2.85 * 10-5 T. (a) Which component of the magnetic field is important when calculating the induced emf in this coil

Explanation:

The coil is rotating about a vertical axis so the plane of the coil must be horizontal . The radius of the coil will cut the vertical component of the earth magnetic field . Due to it a potential difference will be induced between the center of the coil and its circumference . This potential difference will be proportional to speed of rotation of the coil.

The face of coil is lying in horizontal plane so its rotation will not create any change in the flux passing through it as total flux passing through it will remain zero all the time.

Hence it is the  vertical component of earth's magnetic field which is important to calculate induced flux in the coil.

resonant frequency

neither accurate nor precise.