I need a scientific calculator for the iPad; preferably it shows the functions like a real scientific calculator i.e. when you press sin you get sin( on your "display" & not just the result
I suggest PCalc (the lite version is free) or i41CX (really good for hard-core fans of HP calculators)
My favourite calculator app for iOS for some time. Functional, clean interface gets it done. The bit mode is great for algorithm writing with bit manipulations. I think this was one of the first apps I purchased when I got my first iPhone. Still use it daily.
It doesn't do quite what you want when you hit
sin but it does show you, below the answer, that the operation used to compute the answer was
It's available via the App Store. And if it's not free, it's close to it.
Wolfram Alpha has an iPad app. It is admittedly $1.99 from the App Store, but not only will you get basic calculator features, but some pretty serious math and data reference chops in a small package.
It may be overkill for your needs, but the granddaddy of scientific calculation on the iPad is MathStudio, formerly known as SpaceTime. Not just a scientific/graphing calculator, it's a very complete CAS (computer algebra system). And it does use the infix notation you prefer.