Sophisticated implies a level of elegance and intelligent design that might not be present in something that is just complicated. Also, a simple application could potentially be sophisticated if it had a lot of capacity despite its simplicity.
There's a valid reason for this, which is linked to the fact that both mathematics (as a field) and minimum (as a word) are defined by quantities. Per Oxford Dictionary, minimum: (Note the use of "quantity").
The least or smallest amount or quantity possible, attainable, or required.
As defined by the Oxford Dictionary, minimum is a quantitative representation of the smallest amount needed; thus, making it suitable for math and the term minimum angle.
That brings us to minimal, which can be both a qualitative and quantitative characteristic. Thus, depending on whether the user intends to use it qualitatively or quantitatively he or she may be correct. But regardless of the user' intent, using minimal in this sense is subject to misconception.
Per Merriam Webster...
minimal: barely adequate
Per Merriam Webster: (note the use of "quality")
adequate: good enough : of a quality that is good or acceptable
Therefore, minimal is a qualitative characteristic, which contradicts the quantitative nature of math.
To conclude, I admit that minimal can in some instances be synonymous with minimum; however if you consider the dilemma people will encounter (is minimal qualitative or quantitative?), you'll understand why minimum (only quantitative) better represents mathematics. This explains why many have chosen to use minimal angle rather than minimum angle; however, minimum is more technical.
Best Answer
Reward programs use fanciful language to (mis)represent what is going on. But in terms of word definitions:
Claim means to assert that something is yours. In the context of reward programs, this is the "you've already won" case. It is your prize and they are just holding it for you until you demonstrate that you are the rightful owner. That might involve providing a promotional code or giving them your address, phone number, and other personal information to "prove" who you are. See M-W #2.
Again in the context of a rewards program, redeem means to exchange or trade something of value (like a coupon or code) for something else (like a prize or product). It also has a somewhat relevant meaning of to get back something that is or was yours ("you've already won"), by exchanging some placeholder for it (like a a coupon or code). See M-W especially #5b2.