2.12. The normalized radiation intensity of a given antenna is given by

(a) U = sin sin

(b) U = sin 0 sin²

(d) U = sin²0 sin

(f) U = sin² 0 sin³

(c) U = sin 0 sin³

(e) U = sin²0 sin²

The intensity exists only in the 0 ≤ 0 ≤ π,0 ≤ ≤ region, and it is zero elsewhere.

Find the

(a) exact directivity (dimensionless and in dB).

(b) azimuthal and elevation plane half-power beamwidths (in degrees).