You need to keep the NSDate, not just the formatted date. Now you'll want to compare the date the person entered against the zodiacal dates.
This question, How to compare two NSDates: Which is more recent?, show you how to compare dates. A little bit of cut/paste code from that question is:
if ([date1 compare:date2] == NSOrderedDescending) {
NSLog(@"date1 is later than date2");
}
Now you just need to create an NSDate for each sign of the zodiac. I don't know those dates so just google for them. Again, the search function is your friend here. Look at Initialize NSDate with custom date and notice this line:
[calendar dateFromComponents:components]
Be sure to set the years correctly!