To create a field that indicates the day of the week for the Appointment (and later, we'll discuss how to for other objects), navigate to Setup.
In the Quick Find box, search Objects and select Objects under Create.
Navigate to the Appointment object & select 'New' under 'Custom Fields & Relationships'. Your data type will be Formula, and on the next page your Formula Return Type will be Text. 'Appointment Day' is ideal for the field name.
Your formula will be as follows:
CASE( MOD( i360__Start__c - DATE(1900, 1, 7), 7), 0, "7-Sunday", 1, "1-Monday", 2, "2-Tuesday", 3,
"3-Wednesday", 4, "4-Thursday", 5, "5-Friday", 6, "6-Saturday","Error")
Save, and run First Time Setup.
(If you want to visibly see this on the Appointment page, add it to the 'Appointment - Information' field set, and then run First Time Setup, always.)
In order to use this formula on a different object, you'd just have to replace the Appointment date field with a date field from the object you're creating it for. For instance, on the Lead Source, you can create a Taken Day field, and use the Taken On date as part of the formula: