Hi!

I hit a wall on the following trig formula:

Z=arccosin (sin45xsin(-23.50) + cos45Xcos(-23.50)).

After working out the parentheses contents, I get :

Z=arcos-32.50

why does my calculator return an error message for arcos(-32.50), i.e. a neg. number??

For your information, Z is the the Zenith angle, i.e. the angle between the sun's observed position in the sky ( depending on the latitude, the time of the day and the season) and its would-be Zenith position.

Z , in turn, allows to calculate the insolation value ( I) for that latitude , season and time of the day, according to the formula I=SXcosZ, where S is the amount of heat energy received by the Earth ( insolation) when the sun is perpendicular ( 1000w/Sqmt/sec)

In the above formula I have already plugged in those values: the value 45 deg.( sin45) is the latitude I chose , while -23.50 deg. is the solar declination angle corresponding to the winter solstice, as opposed to + 23.50 for the summer solstice.

Thank you for your help

Franco

calculator gives me an error message for the negative value of -23.50 deg., which is the correct solar declination angle on the winter solstice, as compared with + 23 50 deg.value for the summer solstice. I have no problems in detemining Z for + 23.50 deg. Why do I get an error message for a negative value such as -23.50 ?