Calculate the approximate directivity from the half-power beam widths of a unidirectional antenna if the normalized power pattern is given by: (a) Pn = cos θ, (b) Pn = cos^2 θ, (c) and Pn = cos^3 θ. In all cases, these patterns are unidirectional (+z direction) with Pn having a value only for zenith angles 0° ≤ θ ≤ 90° and Pn = 0 for 90° < θ ≤ 180°. The patterns are independent of the azimuth angle φ. Discuss the obtained results.