Longitude of Ascendant and House Cusp Calculation:

 

The ascendant is the same for most house systems, as is the MC (which is not the tenth house cusp in equal house systems). Regiomontanus has the same ASC and MC as Placidus, Campanus, Koch etc.

R = arctan (sin (H) * tan (glat) / cos (RAMC + H)) correct quadrant to be use

Longitude of cusp = arctan ((cos (R) * tan (RAMC + H)/ cos (R + E)) correct quadrant to be use

Blow function will provide correct degree in all Quadrant

    R = DegAtan2(DegSin(H) * DegTan(glat), DegCos(RAMC + H))     

    LCusp = DegAtan2(DegCos(R) * DegTan(RAMC + H), DegCos(R + E))

For cusps:

1.     10 (MC): H = 0

2.     11: H = 30

3.     12: H = 60

4.     1 : H = 90

5.     2 : H = 120

6.     3 : H = 150

7.     4 : H = 180

8.     5 : H = 210

9.     6 : H = 240

10.  7 : H = 270

11.  8 : H = 300

12.  9 : H = 330

Where:

E: obliquity of the ecliptic for the date (23.4523 in 1900; 23.4393 in 2000)
glat: geographic latitude
RAMC: right ascension of MC = 15 * local sidereal time

Example:

Longitude: 77.7 E, Latitude: 28.9833 N, Time Zone: -5.5 Date: 15 Feb 1966 Time : 2:45 AM

Julian day: 2439171.385, JD2000: -12373.614, Obliquity E: 23.44369651.

Local Mean Sidereal Time: 9.586045138, RAMC= 143.7906771

Longitude of Ascendant (Asc) = 258.3515

Longitude of 10^th House / Midheaven / Medium Coeli (MC) = 141.25524