I'm working my way through some 'Graphs of trigonometric functions' on khanacademy.org and came across something that I found to be a little confusing, and I wanted to know if my intuition is correct or not.
The answer the question wanted me to supply was the function:
$$f(x) = 0.5\sin(\pi x − 1.5\pi) + 1.5$$
The answer I provided, but that was rejected was:
$$g(x) = 0.5\sin(\pi x + 1.5) + 1.5$$
If I graph these functions, or write a function on my computer and test against various inputs, these yield slightly different answers.
It appears that $f$ gives me better answers than $g$, but I wasn't sure if this was due to the math, or due to computers.
Are these functions different, or am I just seeing precision errors of using pi on my computer?