radiation pattern of half wave dipole

cn we able 2 find out the directivity in 2d plot of half wave dipole,....i got 8 shaped radiation pattern hw 2 obseve its directivity? i hve given theta range from 0:pi*0.01:2*pi,.and electric field formula e=(cos((pi/2)*cos(theta)))/sin(theta) ,.i am doing in matlab

If you have an 8 shaped pattern, you are doing something wrong. It would suggest you are simulating at a higher frequency. You should get two peaks offosite each other, and two nulls at 90 degrees to the peaks.

The power follows the square of the E field. Integrate the power over 4 pi steradians, noting it is symmetrical in one plane. The integrated power must be 1.0, assuming an input of 1 W. Then find how much greater the peak is, compared to the average.

There are some hints above. It's pointless someone giving you a bit of code to do it, as you wont learn anything.