I sometimes hear these two words used interchangeably.
Problem:
These two words are not synonyms.
Explanation:
The primary definition of the word “determinate” as a verb is to make certain of. The primary definition of the word “determinate” as an adjective is having defined limits.
The primary definition of the word “determinant” as a noun is a determining agent. The primary definition of the word “determinant” as an adjective is having the power of deciding.
I believe that these words most often are used interchangeably because of sloppy pronunciation.
Solution:
When using each of these words as an adjective, think having defined limits for “determinate” and having the power of deciding for ” determinant”.