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HP 48GII Algebraic and RPN Operating Modes
Actually, pressing Y would get the same result, and more quickly. Anyway, this is the sine of the angle between the ladder and
the vertical. Or is it the cosine? Press „¼ and see the answer, 74.91 degrees. No, that is not right, it must be the arc cosine
that you need. You could use ...¯ again to undo the arc sine, but it is quicker to press S, then „¾. Your ladder
would be only 15.09 degrees away from the vertical. That is uncomfortably steep. So try the same calculation for your neighbor's 38
foot ladder.
Type 28†38/ then „¾. You can use the space key † instead of ` to separate two numbers on
the command line, and † is nearer to the numeric keys, so you have to move your finger a shorter distance to type it. When you
press a calculation key afterwards, the HP48GII knows that the space is separating two different numbers. This time the answer is
42.54 degrees. The ladder would be at a shallow angle on the ground and might slip away as you stand on it.
Neither ladder is really suitable. Maybe you should ask some other neighbors if they would lend you a ladder with a better length.
What would be a good length? 30 degrees would probably still be too much, about 20 degrees would be about right. So type the
height again and divide by the cosine of 20 degrees. Type 28`20T/. That gives 29.80. A 30 foot long
ladder would be almost ideal.
The same calculations could be done in Algebraic mode with no difficulty. Nevertheless, many users find that Algebraic mode is less
well suited to such step-by-step calculations, especially because „î must be used repeatedly to bring back the result of the
previous calculation.
Once all the examples have been completed it may be worth returning the calculator to its normal modes. It can also be helpful to
clear the stack by pressing ...·.
The Operating Mode
The examples and explanations in this training aid have used only real numbers, but the same principles apply with complex
numbers, vectors, matrices, lists of numbers, and other objects. Whether you use Algebraic mode or RPN mode, the stack is a basic
tool. The combination of stack and Algebraic or RPN mode is so important in the use of the HP48GII that Algebraic or RPN is called
the calculator's Operating Mode – it is the way in which the calculator operates.
These examples have shown how the user can switch between the two modes as necessary, but the modes can be combined
further. Results on the stack from RPN mode calculations can be put in Algebraic calculations with the ANS command, and results
from Algebraic calculations are on the stack ready for use if the calculator is switched to RPN mode. RPN mode works with all kinds
of objects on the stack, even programs and algebraic expressions. To put an algebraic expression on the stack in RPN, press the
³ key first and then type the algebraic expression and `. That expression can then be used in RPN calculations, or plotted or
solved. The Algebraic mode and the RPN mode need not be treated as exclusive, one or the other; it is possible to treat them as
complementary and use whichever one suits a given task best.
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HP 48GII Algebraic and RPN Operating Modes
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