It is short for sine (pronouncing it as sin annoys many maths teachers). Check this site out for detailed info. http://www.clarku.edu/~djoyce/trig/
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You need a scientific calculator, or one with function keys.
A Texas Instruments graphing calculator can be used as a basic calculator, a scientific calculator and a graphing calculator.
No.
Usually a graphing calculator should have all the capabilities you expect from a scientific calculator (and more, since it does the graphing). For more details, check the manual of your calculator if you already have one.
A graphing calculator is a scientific calculator with a graphing display window. Otherwise, there are no limits to the type of calculations that can be made on either of them.