HP 35s User Manual

							 
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HP 35s  Temperature Conversions 
 
hp calculators - 5 - HP 35s  Temperature Conversions - Version 1.0 
Other temperature scales 
 
A temperature scale with 100 degrees between two points is called a centigrade scale (“centigrade” means one hundred 
degrees), and is an obvious scale for use in the metric system where measurements are based on powers of 10. A scale 
with 0 at the freezing point of water and 100 at the boiling point was suggested by Celsius, and is now called the Celsius 
scale. The Fahrenheit scale is the best known alternative, but some old textbooks (especially French ones) use the 
Reaumur scale, with the freezing point of water at 0 degrees and the boiling point at 80 degrees. 
 
The Kelvin and Rankine temperature scales avoid the complication of Absolute Zero not being called 0. Kelvin degrees 
are the same size as Celsius degrees, but Absolute Zero is 0 degrees Kelvin. Rankine degrees are the same size as 
Fahrenheit degrees but again Absolute Zero is 0 degrees Rankine. 
 
Temperatures can therefore be converted using these expressions: 
 
T°K ! T°C + 273.15°C 
 
T°R ! T°F + 459.67°F 
 
T°K ! T°R × 5/9 
 
The symbol ! means “is equivalent to”, so the first expression means that a temperature of T°C can be converted to an 
equivalent temperature in degrees Kelvin by the addition of 273.15. 
 
Using equations and programs for complicated conversions 
 
For complicated conversions, it can be useful to write an equation or a program to do the conversion automatically. 
 
Example 4: Write an equation to convert degrees Fahrenheit to degrees Kelvin. 
 
Solution: Assume that the temperature in Fahrenheit will be in the variable F. To enter the equation, equation mode 
is first entered by pressing 6, and the expression is typed as follows: 
 
 7894#$:;%&5
						

							 
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HP 35s  Temperature Conversions 
 
hp calculators - 6 - HP 35s  Temperature Conversions - Version 1.0 
 Figure 7 
 
:1> should be typed, and the equation will run for a moment, then the answer will be displayed. 
 
 Figure 8 
 
Answer: The answer, 305.372 degrees Kelvin, is displayed.
 
The equation can now be used again to convert a different temperature from degrees Fahrenheit to degrees Kelvin. 
Press 6, to enter equation mode again, press 2 to start the equation again, type the temperature in degrees 
Fahrenheit, and press > to carry out the calculation. 
 
Programs can be used instead of equations if the user prefers to use programs or if the additional power of program 
commands such as test and loops is needed. How to write programs is described in a separate training aid. 
   
						

							 
 
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HP 35s  Angular conversions and arithmetic 
 
 
 
 
Angular measurements 
 
Time measurements 
 
Practice solving problems involving angles and times 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
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HP 35s  Angular Conversions and Arithmetic 
 
hp calculators - 2 - HP 35s  Angular Conversions and Arithmetic - Version 1.0 
Angular measurements 
 
There are two primary ways of measuring angles, radians and degrees (there is a third way, Grads, which is not used as 
often). Radians measures the span of an angle in terms of the unit circle, where a full revolution involves an angle of 2!. 
Degrees measures the span of an angle where a full revolution involves an angle of 360 degrees. The HP 35s calculator 
can work with angles in either measurement system and provides the ! and #$ functions to convert 
between them. 
 
Angles are also sometimes measured in degrees using two different formats: decimal degrees and degrees, minutes, 
and seconds. In decimal degrees, an angle might simply be 33.5 degrees. In the degrees, minutes, seconds (or DMS) 
format, an angle might be 30 degrees, 15 minutes, 10 seconds. An angle in the DMS format has a degree broken down 
into 60 minutes and each minute broken down into 60 seconds. The HP 35s calculator can convert between these two 
formats of angles in degrees using the #% and !5 functions. Note that these functions are actually 
Hours Minutes Seconds and Hours conversions, but work for angle conversions between decimal degrees and DMS. 
 
Time measurements 
 
A useful application of the conversion between decimal degrees and DMS angles is that the exact same conversion can 
also work for time. A measurement of 10.5 hours can be converted into 10 hours and 30 minutes by the same process 
an angle of 10.5 degrees can be converted into 10 degrees, 30 minutes.  
Practice solving problems involving angles and times  
Example 1: Convert an angle of 100 degrees into radians.  
Solution: In RPN mode: &! 
 In algebraic mode: !&( 
 
 Figure 1  
Answer: 1.7453 radians.  Figure 1 shows the display assuming algebraic mode.  
Example 2: Convert an angle of 1.5 radians into decimal degrees. 
 
Solution: In RPN mode: &)*#$ 
 In algebraic mode: #$&)*( 
 
 Figure 2 
 
Answer: 85.94 degrees.  Figure 2 shows the display assuming algebraic mode. 
 
Example 3: Add an angle of 30.5 degrees to an angle of !/4 radians and express the answer in radians. 
 
Solution: In RPN mode: +)*!!,-./ 
 In algebraic mode: !+)*0/!,.-(   
						

							 
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HP 35s  Angular Conversions and Arithmetic 
 
hp calculators - 3 - HP 35s  Angular Conversions and Arithmetic - Version 1.0 
 Figure 3 
 
Answer: 1.3177 radians. Figure 3 shows the display assuming algebraic mode. 
 
Example 4: Convert an angle of 20.67 decimal decrees to an angle format of DMS. 
 
Solution: In RPN or algebraic mode: 1)23#%4
 In algebraic mode: #%1)23( 
 
 Figure 4 
 
Answer: The equivalent measurement in DMS is 20 degrees, 40 minutes and 12 seconds. Figure 4 shows the  
 display assuming RPN mode. 
 
Example 5: Add 5 hours 33 minutes to 3 hours 58 minutes. 
 
Solution: Each measurement of time will need to be converted from the Hours Minutes Seconds format into 
 an equivalent "decimal hours" format and then added together. 
 
 In RPN mode: *)++!5+)*5!5/#% 
 In algebraic mode: #%!5*)++0/!5+)*5( 
 
 Figure 5  
Answer: The answer is 9 hours, 31 minutes.  
Example 6: What is the size of the angle formed by joining an angle of !/5 radians and an angle of 40.62 degrees.   
 Express the answer in DMS format.  
Solution: In RPN mode: !,*.#$-)21/#% 
 
 In algebraic mode: #%#$!,.*0/-)21( 
 
 Figure 6 
 
Answer: The resulting angle is 76 degrees, 37 minutes and 12 seconds. Figure 6 shows the  
 display assuming algebraic mode.   
						

							 
 
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HP 35s  Using Calculator Memories to  
Help Solve Problems 
 
 
 
 
Variables and Memory Registers 
 
Practice Examples:  
 
Storing and Using a Constant 
 
Storing a Temporary Result 
 
Exchanging and Viewing Registers 
 
Other Operations with Memory Registers 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
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HP 35s  Using Calculator Memories to Help Solve Problems 
 
hp calculators - 2 - HP 35s  Using Calculator memories to Help Solve Problems - Version 1.0 
Variables and Memory Registers 
 
When an equation is typed on the HP 35s, it can use variables with names from A through Z. For example an equation 
 
3X² - 5X= A 
 
has the variables X and A in it. 
 
Variables can also be used in programs and in calculations from the keyboard. 
 
Each variable consists of a number and of a place in the calculator memory where the number is stored. 
 
The number is called the value of the variable. If no value has been give to a variable then its value is 0. 
 
The place in memory where this number is stored is called a data register, or a memory register, or just a memory. 
 
Each memory register can be referred to by a numeral as well as by its name. Register A is -1 and register Z is -26. Six 
more registers can be referred to by numerals and hold values from statistics calculations. Two of the lettered variables 
are special “index” registers, which are explained in another training aid. The names “data register” or “memory register” 
or “memory” refer to all of these, not just the variables, so these names are often used in this training aid, rather than the 
name “variables.” 
 
In many cases it is helpful to use variable names as mnemonics, for example D for density or P for pressure, but when 
registers are used to store a table then names are meaningless and the numeral for each register is what counts. 
 
This training aid shows ways in which memory registers can be used. A separate training aid covers the special topic of 
how arithmetic can be carried out directly in memory registers and using the memory registers. 
 
Practice Example: Storing and Using a Constant 
 
The HP 35s provides a set of physical constants, such as the speed of light. The conversion functions also provide 
constants to convert between metric and imperial measurements. Users who need to store other constants can put them 
into the memory registers so they can be easily used in calculations. 
 
Example 1: An engineer is working with a type of concrete that has a density of 149.8 lb/ft³ (Different types of concrete 
have different densities, so the density of concrete is not a physical constant provided by the HP 35s!) 
Store the density of this concrete in a data register and use it to calculate the mass of a concrete beam 2 ft 
by 1.5 ft by 20ft. 
 
Solution: Type the density, then press !! and a variable name to store the density in that variable’s memory 
register. To store a density of 149.8 in variable D, press these keys. 
  
 #$%&!!( 
  
 When !! is pressed, the symbol “A..Z” appears at the top of the screen. This tells the user that the 
next key pressed should be one of the keys with letters A to Z at their lower right, and that the 
corresponding letter will be used. For the letter “D”, press the 9 key. 
    
						

							 
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HP 35s  Using Calculator Memories to Help Solve Problems 
 
hp calculators - 3 - HP 35s  Using Calculator memories to Help Solve Problems - Version 1.0 
 To calculate the mass, multiply the length by the width by the height. Then recall the number from D and 
multiply by that. In RPN mode, press the keys: 
  
 )(%*+),+-+ 
  
 In algebraic mode, press: 
  
 )+%*+),+-( 
  
 Figure 1 
 
Answer: The beam has a mass of 8,988 pounds. This value of the variable D can be used for further calculations. If 
a different type of concrete is selected, the density of this new type can be stored in D and the calculations 
can be repeated. The value in D is not lost when the calculator is turned off. 
 
Note: The recall and the multiplication can be combined into one command RCL!D. A separate training aid describes 
using arithmetic with the memory registers. 
 
Practice Example: Storing a Temporary Result 
 
The memory registers are available separately from the memory in which ordinary calculations are carried out. In 
algebraic mode, up to thirteen levels of brackets can be used, together with numbers saved with the brackets. RPN 
mode has four stack registers, X, Y, Z and T, and also the LastX register, often called L. The memory registers are 
separate from these. Note that the variables named L, T, X, Y and Z are not the same as the stack registers with these 
names, and that the Exponent key . and the Cancel key / do not access the variables with these names. 
 
If a calculation is more complicated than the algebraic or RPN rules allow, temporary results can be stored in memory 
registers, and can then be used later. 
 
Temporary results can also be stored in memory registers just to make a calculation easier, as in this example. 
 
Example 2: The formula below uses the expression (0.2 + sin(35°)) three times. In algebraic mode, it would be difficult 
to re-use this expression without typing it in each time. In RPN mode the expression could be calculated 
once, then kept on the stack and re-used as needed, but this would require keeping track of which number 
is where on the stack. 
 
 Figure 2 
 
Solution: The expression uses degrees, so set Degrees mode if it is not already set. (To do this press 9.) 
First calculate the expression that is used several times and store its value in a memory register. In this 
example, use register V for the value of the expression. Then calculate the whole formula, recalling the 
value each time it is needed. 
    
						

							 
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HP 35s  Using Calculator Memories to Help Solve Problems 
 
hp calculators - 4 - HP 35s  Using Calculator memories to Help Solve Problems - Version 1.0 
 In algebraic mode, type the expression like this: 
  
 %)012*( 
  
 Figure 3 
  
 Then store it in register V by typing: 
  
 !!3( 
  
 Figure 3 
  
 Now the main formula can be calculated. First calculate the top line at the left-hand of the formula. The 
value of the expression is still available, so there is no need to recall it, but to see how it all works, recall V, 
calculate its arc sine and multiply by 5: 
  
 !4-3+* 
  
 Next, divide by the arc cosine of the expression, recalling it again from V: 
  
 5!6-3 
  
 Figure 4 
  
 Now multiply by the square root of three times the expression.  
  
 +72+-3 
  
 Figure 5 
  
 Finish the calculation by pressing (: 
  
 Figure 6 
 
Answer: To four decimal places the complete formula evaluates to 9.8159. Calculation was considerably easier, and 
the expression displayed on the upper line is simpler, because the temporary value was stored in a 
memory register.