Final answer:
Changes made with pure functions in programming ensure functions are predictable and maintainable by always returning the same output for the same input without side effects. Sine, cosine, logarithms, and exponential functions used in equations require dimensionless numbers for purity.
Step-by-step explanation:
When we say that 'changes are made with pure functions', we are typically referring to the concept of functional programming.
In this context, a pure function is a function that given the same input will always return the same output without causing any side effects - that is, it does not alter any state or data outside its scope.
Pure functions are a fundamental part of writing predictable and maintainable code in many programming languages. Functions like sine and cosine, logarithms, or exponential functions must take in dimensionless numbers and return dimensionless numbers to remain pure.