HP 35s User Manual

							 
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HP 35s  Solving Trigonometry Problems 
 
hp calculators - 3 - HP 35s  Solving Trigonometry Problems - Version 1.0 
Solution: In RPN mode, calculate !/2, then press . 
 
 ./0. 
 
 In algebraic mode, press  then calculate !/2. 
 
 ./0-.  
 
 Figure 2 
 
Answer:  The sine of !/2 radians is calculated as exactly 1 
 
Example 3: Show that the rule sin²(x) + cos²(x) = 1 applies correctly when x is 30°. 
 
Solution: First, remember to set the required angle mode. Press 9&. 
 
 In algebraic mode: 
 
%12(3**412!(3-%
%
 Figure 3 
 
 In RPN mode: 
 
%(312(3!124%
 
 Figure 4 
 
Answer: Both the algebraic and the RPN calculations confirm that the rule sin²(x) + cos²(x) = 1 applies correctly 
when x is 30°.  
 
Example 4: A designer wants to use triangular tiles with sides 3 inches, 5 inches and 7 inches long, to put a mosaic on 
a floor. What is the angle opposite the 7 inch side? Will it be possible to lay three tiles next to each other 
with this angle pointing inwards? 
 
Solution: Use the cosine rule to calculate the angle. The cosine rule states that for any triangle with sides a, b and c, 
and angle A facing side a: 
 
  Figure 5 
 
From this, A can be calculated as:   
						

							 
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HP 35s  Solving Trigonometry Problems 
 
hp calculators - 4 - HP 35s  Solving Trigonometry Problems - Version 1.0 
 
   Figure 6 
 
 In RPN mode, the calculation can be done like this: 
 
 512(1246127050(018%
 
 In algebraic mode, calculate: 
 
%184125*412(*7126**0050(-%
 
 Figure 7 
 
Answer:  The angle opposite the 7 inch side is 120 degrees. This means that three tiles will fit together exactly with 
this angle pointing inwards, as they would make up 360 degrees. 
 
Example 5: A ladder is leaning against a vertical wall. The ladder is 6 meters long and the foot of the ladder is 3 meters 
from the base of the wall. What is the angle between the top of the ladder and the wall? 
 
Solution: In RPN mode, divide the side opposite the angle by the long side and get the arc sine: 
 
 (-901: 
 
 In algebraic mode, press: 
 
 1:(09-.%
 
 Figure 8 
 
Answer:  The ladder is at an angle of 30 degrees from the wall. 
 
Example 6: A vector has components –5 in the X direction and –8 in the Y direction. In what direction does it point? 
 
Solution: It would be possible to divide –5 by –8 and calculate the arc tangent, giving approximately 32 degrees, but 
this would not specify the quadrant in which the vector lies. Fortunately, the 35s complex display modes 
provide a way to view the complete arc tangent function that recognizes in which quadrant an angle lies. 
 
 The solution is the same in either RPN or algebraic mode.  
 
 First, set the display mode to ra.    
						

							 
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HP 35s  Solving Trigonometry Problems 
 
hp calculators - 5 - HP 35s  Solving Trigonometry Problems - Version 1.0 
 Then, enter the Y magnitude, press the 6 key, and enter the X magnitude. Then press -. 
 
 ;
						

							 
 
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HP 35s  Solving systems of linear equations 
 
 
 
 
Systems of linear equations 
 
Using the built-in solver equations  
 
Practice solving linear systems 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
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HP 35s  Solving systems of linear equations 
 
hp calculators - 2 - HP 35s  Solving systems of linear equations - Version 1.0 
Systems of linear equations 
 
A system of linear equations is a set of linear equations involving two or more variables. A basic problem is to determine 
if there are values for the variables that will allow each equation in the set to be solved so that the left side of the 
equation equals the right side of the equation. Linear systems appear in many applications such as forecasting, 
optimization, etc. Systems are often described as 2x2, 3x3, 4x4, etc., referring to the number of variables and the 
number of equations in the set. 
 
An example of a 2x2 linear system might be: 
 
3 X +    Y = 10 
   X – 2 Y = 8 
 
which has the solution set of { X = 4, Y = -2 }. Not every system of linear equations has a solution. Other systems have 
an infinite number of solutions. 
 
Using the built-in solver equations 
 
The HP 35s two build-in solver equations to find solutions to 2x2 and 3x3 linear systems. These can detect situations 
where no solution exists or where an infinite number of solutions exist. These solver equations are part of the HP 35s 
ROM and are always present at the top of the equation list. If you press !, then the two equations should be visible 
as shown below (if you have entered equations of your own, then you may need to use the up or down cursor keys to 
move through the equation catalog to find them):  
 Figure 1 
 
The equation at the bottom of the display is the one that will be solved when #$is pressed.  
 
These equations store the values from the linear system into the lettered variables/registers beginning with A. 2x2 
systems require a total of 6 coefficients to be entered. In this example system, 
 
3 X +    Y = 10 
   X – 2 Y = 8 
 
the coefficient 3 (from the 3 X term) would be stored into A, the 1 (from the implied 1 in front of the Y term) would be 
stored into B, the constant 10 would be stored into C, the 1 (from the implied 1 in front of the X in the second linear 
equation) would be stored into D, the -2 into E, and the 8 into F. 
 
A 3x3 system would use a total of 12 lettered variables/registers, A through L.  
Practice solving linear systems  
Example 1: Solve the 2x2 linear system: 
 
3 X +    Y = 10 
   X – 2 Y = 8    
						

							 
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HP 35s  Solving systems of linear equations 
 
hp calculators - 3 - HP 35s  Solving systems of linear equations - Version 1.0 
Solution: In either RPN or algebraic mode, make sure the 2*2 lin. solve” equation is shown at the bottom of the 
equation screen and press # equation is. The display should appear like the one below before 
beginning the solution by pressing #.$ 
 Figure 2 
$
 Figure 3 
 
 The HP 35s prompts you to enter the value of the first coefficient. It displays the current contents of the A 
register in case you wish to use it again. If you have previously stored a value into A, it may not show 
0.0000 as depicted above.   
 In RPN or algebraic mode:$%&$
$
 Figure 4 
 
 The HP 35s now prompts for the second coefficient which it will store in B.  
  
 In RPN or algebraic mode:$&$
 
 Continue to enter the remaining coefficients as below. 
 
 In RPN or algebraic mode:$(&$
$In RPN or algebraic mode:$& 
$In RPN or algebraic mode:$)*& 
$In RPN or algebraic mode:$+& 
 
 After entering the last coefficient, the HP 35s displays the solution found beginning with X, as shown below. 
To view the solution for Y, press the down cursor key, ,. 
$
 Figure 5 
$
 Figure 6 
 
   
						

							 
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HP 35s  Solving systems of linear equations 
 
hp calculators - 4 - HP 35s  Solving systems of linear equations - Version 1.0 
Answer: The system has the solution X = 4, Y = -2. 
 
Example 2: Solve the 3x3 linear system: 
 
 4 X +     5 Y +     Z = 0 
 3 X +     2 Y  -     Z = 7 
-1 X + 112 Y +  3 Z = 127 
. 
Solution: In either RPN or algebraic mode, make sure the 3*3 lin. solve” equation is shown at the bottom of the 
equation screen and press # equation is. The display should appear like the one below before 
beginning the solution by pressing #.$ 
 Figure 7 
$
 Figure 8 
 
 As in the previous example, key in each coefficient and press &. The keystrokes are the same in RPN 
or algebraic mode. 
  
 -&$$(stored into A)$
 .&$$(stored into B)$
 &$$(stored into C)$
 (&$$(stored into D)$
 %&$$(stored into E)$
 )&$$(stored into F)$
 *&$$(stored into G)$
 /&$$(stored into H)$
 *&$$(stored into I)$
 )&$(stored into J)$
 %&$$(stored into K)$
 )/&$(stored into L)$
 
 After entering the last coefficient, the HP 35s displays the solution found beginning with X, as shown below. 
To view the solution for Y and Z, press the down cursor key, ,. 
$
 Figure 9 
$  
						

							 
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HP 35s  Solving systems of linear equations 
 
hp calculators - 5 - HP 35s  Solving systems of linear equations - Version 1.0 
 Figure 10 
$
 Figure 11 
 
 To view the solutions as fractions, when X, Y, and Z are displayed, press 0$and the results are 
shown as: 
$
 Figure 12 
$
 Figure 13 
$
 Figure 14 
 
Answer: The solution to the system of linear equations is { X = -3/11, Y = 1 3/11, Z = -5 3/11 }