when Dundee was classed as to be in Forfarshire, now Angus.
Sorry, but this is a case of accurate information being potentially misleading!
The city of Dundee was always in the County of Angus.
However some time in the 18th century someone decided to 'rationalise' the names of (some of) the Scottish counties by renaming them after their respective county towns. The county town of the county of Angus is Forfar, so Angus became Forfarshire to officialdom, but not universally to its inhabitants. The Statistical Account uses both names, and natives of the county often state in census etc that they were born in Angus.
In 1928 this change of official name was reversed by Act of Parliament and the county reverted to its ancient name of Angus for all official purposes.
It was not until the reorganisation of local government in 1975 that the City of Dundee council was made independent of the rest of Angus. At the same time all the historic counties were abolished as local authority areas, but they remain in existence as ceremonial counties.
So in general, for historical research purposes, Dundee is in Angus. Forfarshire, bar the odd minor adjustment of a boundary here and there, is synonymous with Angus. Angus is the ancient and traditional name.
The only time you need to know what place is in which modern local government area is if you are looking for records which may be in the care of the present local authorities - the obvious one being burial records.