HP 35s User Manual

							 
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HP 35s  Hyperbolic functions 
 
hp calculators - 3 - HP 35s  Hyperbolic functions - Version 1.0 
Solution: The travel time is given by the following formula: 
 
  t =       437    x      tan (63 degrees)        
  135 x ASINH (tan (63 degrees) ) 
 
 Assuming the 35s is in Radians mode, change it to Degrees mode to calculate the tangent value.   
 Assuming RPN mode: 9& (Sets Degrees mode) 
%()*+(,-.!/&(0-1%
%
 Figure 4 %
 Assume algebraic mode: 9&  (Sets Degrees mode) 
%()-,+(#14&(0-!/,+(*%
 
 Figure 5  
Answer: The travel time between the peaks is just under four and one half minutes. Figure 4 shows the display 
 in RPN mode, while Figure 5 shows the display in algebraic mode.  
Example 3: A cable is strung between two poles that are 40 feet apart, with the cable attached to each pole at a  
 height of 30.436 feet above the level ground. At the midpoint between the poles, the cable is 18.63  
 feet above the level ground. What is the length of the cable required between the two poles? %
Solution: The length of the cable is described by the formula below, where a is the lowest height of the cable and 
 D is the distance between the two poles:  
 L = 2 a SINH ( (D/2) / a )  
 Assuming RPN mode 
%2*#1&34+(1.5!$5#--%
 
 Figure 6  
 Assuming algebraic mode 
%!$21#1&34+(#-#-&34+(*%
 
 Figure 7   
Answer: The length of the cable will be 48.14 feet.   
						

							 
 
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HP 35s  Solving for roots 
 
 
 
 
Roots of an equation 
 
Using the SOLVE function 
 
Practice solving problems involving roots 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
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HP 35s  Solving for roots 
 
hp calculators - 2 - HP 35s  Solving for roots - Version 1.0 
Roots of an equation 
 
The roots of an equation are values of X where the value of Y is equal to zero. For example, the equation Y = X – 2 has 
a real root at the value +2. The equation Y = X2 – 9 has real roots at the values of + 3 and – 3. Not every equation has 
roots that are real numbers. For example, the equation Y = X2 + 4 has no real roots, meaning there are no real values for 
X that will cause X2 + 4 to equal zero. 
 
Using the SOLVE function 
 
The HP 35s has a very powerful root finding capability built into its SOLVE function. As applied in this training aid, the 
SOLVE function, accessed by pressing the ! key, will be used to find roots from user-written programs computing 
the value of a function. This will involve entering a small program, keying in a small equation into the program using a 
variable, indicating to the HP 35s which variable is being considered as the current function, and then solving for the 
value of that variable when the function is equal to zero. The HP 35s knows which variable to solve for by setting the 
value of the function under consideration using the # function. To indicate to the HP 35s that the variable X is to 
be used, press #$. 
 
This training aid cannot begin to illustrate the wide range of applications available using the built-in solver, but it can 
illustrate some of the more common uses.  
Practice solving problems involving roots  
Example 1: Solve for the roots of Y = X2 – 4  
Solution: Were looking for values of X such that X2 – 4 = 0. First, well enter a program that computes the value of 
the function. If a program already exists in program memory with the name of X, then it will need to be 
cleared. This can be done by pressing %& to have the HP 35s display the list of 
programs in the calculator and then press ( to step through the program labels. When the label of the 
program to be deleted is shown in the display, pressing )*will delete that program from the 
calculators memory. Pressing + will then clear the display and allow you to proceed. 
 
 In RPN or algebraic mode:  ),)-$./$01234
4454
 
 Figure 1 
 
 To show the checksum and length of this program, press the following in RPN or algebraic mode. Note that 
the symbol &4means to press the right arrow cursor key. 
4
4In RPN or algebraic mode: %&6  
 Figure 2 
  
   
						

							 
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HP 35s  Solving for roots 
 
hp calculators - 3 - HP 35s  Solving for roots - Version 1.0 
 If the checksum of the program just entered does not equal 8B27, then you have not entered it correctly. To 
clear the checksum display press:  
 
 In RPN or algebraic mode: ),  
 
 Then, to exit the program environment, press: 
 
 In RPN or algebraic mode: ), 
 
 Store an initial guess for X of 10 into the variable X. Then set the function to X and solve for the value of X.  
 
 In RPN or algebraic mode:  78)9$#$)!$4
 
 Figure 3 
 
 Since you feel this equation has a negative root as well, store a new guess for X of -10 into the variable X. 
There is no need to set the function to X (since it has already been done). Solve for the value of X.  
 
 In RPN or algebraic mode:  78:)9$)!$4
 
 Figure 4 
 
Answer: Roots found for the equation are –2 and +2.   
Example 2: Solve for the roots of Y = X2 – 7X + 12  
Solution: Were looking for values of X such that X2 – 7X + 12 = 0. First, well enter a program that computes the 
value of the function. If a program already exists in program memory with the name of X, then it will need to 
be cleared. This can be done by pressing %& to have the HP 35s display the list of 
programs in the calculator and then press ( to step through the program labels. When the label of the 
program to be deleted is shown in the display, pressing )*will delete that program from the 
calculators memory. Pressing + will then clear the display and allow you to proceed. 
 
 In RPN or algebraic mode:  ),)-$.4
44/$012;
						

							 
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HP 35s  Solving for roots 
 
hp calculators - 4 - HP 35s  Solving for roots - Version 1.0 
4
4In RPN or algebraic mode: %&6  
 Figure 6 
 
 If the checksum of the program just entered does not equal 1086, then you have not entered it correctly.  
 
 To clear the checksum display press:  
 
 In RPN or algebraic mode: ),  
 
 Then, to exit the program environment, press: 
 
 In RPN or algebraic mode: ), 
 
 Store an initial guess for X of 10 into the variable X. Then set the function to X and solve for the value of X.  
 
 In RPN or algebraic mode:  78)9$#$)!$4
 
 Figure 7 
 
 Since you feel this equation might have a root larger than this, store a new guess for X of 100 into the 
variable X. There is no need to set the function to X (since it has already been done). Then solve for the 
value of X.  
 
 In RPN or algebraic mode:  788)9$)!$4
 
 Figure 8 
 
 The same root is returned. This is a good indication (but certainly not foolproof) that there are no roots 
larger than +4 for this equation. 
 
 To see if there is a root less than +4 for this equation, store a new guess for X of –10 into the variable X. 
Then solve for the value of X.    
						

							 
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HP 35s  Solving for roots 
 
hp calculators - 5 - HP 35s  Solving for roots - Version 1.0 
 In RPN or algebraic mode:  78:)9$)!$4
 
 Figure 9 
 
Answer: Roots found for the equation are +3 and +4. Note that the HP 35s owners manual provides much more 
information about providing initial guesses for the SOLVE feature.   
						

							 
 
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HP 35s  Base conversions and arithmetic 
 
 
 
 
Numbers in different bases 
 
Practice working with numbers in different bases 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
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HP 35s  Base conversions and arithmetic 
 
hp calculators - 2 - HP 35s  Base conversions and arithmetic - Version 1.0 
Numbers in different bases 
 
Most numbers we work with day-to-day are in base 10. There are applications within the computer world that require the 
use of numbers in other bases. The number 24 in base 10 can be translated into base 16 by the following procedure. 
Just as each digit’s location in base 10 can be thought of as a power of ten (the ones’ place, the tens’ place, the 
hundreds’ place, etc), each digit’s location in base 16 can be thought of as a power of 16. Each digit in a base ten 
number can hold a value from 0 to 9. In base 16, each digit can hold a value from 0 to F, where F corresponds to the 
value 15 in a base 10 number. Translating 24 from base 10 to base 16 would require a 1 in the second location of the 
base 16 number (and would convert 16 of the 24 number’s value) and an 8 in the second location of the base 16 
number. Therefore, 24 base 10 is equal to 18 in base 16. A similar process could be used to convert 24 base 10 to base 
8 or base 2. 
 
On the HP 35s, numbers can be represented in bases 2, 8, 10 and 16, or binary, octal, decimal and hexadecimal. The 
HP 35s can work with numbers in bases 2, 8 and 16 that are 36 bits in length or less. Since the leftmost bit is used to 
indicate a negative number, the largest positive binary number is 0 followed by thirty-five 1s. This means that the largest 
hexadecimal number that can be entered or generated as an answer is 7FFFFFFFF, (equal to 34,359,738,367 in base 
10, and 377777777777 in base 8). This is because the HP 35s uses a 36 bit binary word space to represent numbers in 
these different bases. Decimal numbers are not limited in this fashion, since they can be represented as floating point 
numbers. 
 
In RPN mode, the third row of keys on the HP 35s ( ! through  ) can be used to enter the hexadecimal digits A 
through F. In algebraic mode, it is necessary to press # and then the appropriate letter key to enter these digits. 
 
The HP 35s calculator provides the ability to easily work with numbers in different bases, as the following sample 
problems illustrate. 
 
Note: Numbers entered into the HP 35s are assumed to be decimal numbers, regardless of the base mode, unless the 
proper suffix of “b”, “o”, or “h” is supplied. These suffix characters are found in the BASE menu as choices 5 through 8, 
and are shown below in Figure 1. It is not necessary to enter the “d” for decimal numbers, except for clarity in a program. 
 
 Figure 1 
 
Practice working with numbers in different bases 
 
Example 1: Convert 4000 base 10 to a base 8 octal number. 
 
Solution: The keystrokes to do this are the same for both RPN and algebraic modes. First, make sure the  
 HP 35s is in DEC mode to enter the base 10 number. 
 
 $%&
()))$%*
 
 Figure 2