Misunderstanding Maths

Bengt and Alban are doing some calculations. Actually, Alban is doing some sort of homework, and Bengt is playing around with his calculator. Bengt tries to draw a graph, of sin²(x), but he has done something terribly wrong. The curve he gets looks a lot like k*sin(x), where k ≈ 0.841470985.
"This calculator is stupid." says Bengt.
"I think it's probably you who's made a mistake." replies Alban.
"I know that, you silly engineer. But it has a resolution of 96x64 pixels. I'm pretty sure my digital watch from the eighties has a higher resolution."
"Yeah, that is stupid. Anyway, I'm having some problems too."
"Good ones?"
"Maybe to you. It says here that the results are in the interval k ± s. But when I look at them, it seems that only a fraction f of them are."
"Interesting. What's f?"
"It's two thirds, I think… or maybe just a little more."

1. What has Bengt done wrong?
2. Is the curve that Bengt has found actually a constant times sin(x)?
3. What is causing Alban's confusion? And what is f?