How to find what day of the week for any given date using Cocoa

You may have a look to the NSDate and NSCalendar classes. For example, here and here

They provide the following code:

NSDate *today = [NSDate date];
NSCalendar *gregorian = [[NSCalendar alloc]
                         initWithCalendarIdentifier:NSGregorianCalendar];
NSDateComponents *weekdayComponents =
                [gregorian components:(NSDayCalendarUnit | NSWeekdayCalendarUnit) fromDate:today];
NSInteger day = [weekdayComponents day];
NSInteger weekday = [weekdayComponents weekday];