I am taking AP Music Theory at school, and today, during a diagnostic test, I came upon a question that I have never encountered. I was to name the scale degree name for a chord, consisting of C#, E, and G#. The key signature had 1 sharp (meaning it was either G Major or e minor), but I had no clue how to fit the chord in. It was not one of the regular ones.
Well if you don't know the key signature (whether it's in the relative major or minor), you could try to see what the scale degree would be in both G major and E minor.
In G major, the root would be the sharp fourth, a scale degree only found in Lydian. Also, #iv triad wouldn't really be found often in music, to my knowledge.
In E minor, the root would be the the submediant. Even though in E minor the C and G are natural, it still is a chromatic mediant, a relationship more commonly found. Therefore, I'd assume the answer would be submediant.
My school doesn't have AP Music Theory, so I don't really know how the class teaches theory, but given the minimal context you were given, you'd have to make some assumptions to come to a clear answer.
The chord consisting of C♯ E and G♯ is C♯minor. Not diatonic to G major or E minor. C minor would be iv in key G, so it could be assumed that it would be #iv, or iv#.
If the key sig. actually meant E minor, then in the melodic minor scale, there is a C♯, but no G♯, so I discount that.