Friday, July 15, 2022

TI-58/TI-59 Week: Law of Cosines

TI-58/TI-59 Week:  Law of Cosines


Introduction


[ A ]:  stores either the angle θ or a 

[ B ]:  stores the length of side b

[ C ]:  stores the length of side c


[ D ]:  calculates the length of side a:

a^2 = b^2 + c^2 - 2 * b * c * cos θ


[ E ]:  calculates the angle θ

cos θ = (b^2 + c^2 - a^2) / (2 * b * c)


The angle θ is opposite slot of side a.


Program Listing


000 76 LBL

001 11 A

002 42 STO 

003 01 01

004 92 INV SBR (RTN)


005 76 LBL

006 12 B

007 42 STO

008 02 02

009 92 INV SBR


010 76 LBL

011 13 C

012 42 STO

013 03 03

014 92 INV SBR


015 76 LBL

016 14 D

017 43 RCL

018 02 02

019 33 x^2

020 85 +

021 43 RCL

022 03 03

023 33 x^2

024 75 -

025 02 2

026 65 ×

027 43 RCL

028 02 02

029 65 ×

030 43 RCL

031 03 03

032 65 ×

033 43 RCL

034 01 01

035 39 cos

036 95 =

037 34 √

038 42 STO 

039 04 04

040 INV SBR


041 76 LBL

042 15 E

043 53 (

044 43 RCL

045 02 02

046 33 x^2

047 85 +

048 43 RCL

049 03 03

050 33 x^2

051 75 -

052 43 RCL 

053 01 01

054 33 x^2

055 54 )

056 55 ÷

057 53 (

058 02 2

059 65 ×

060 43 RCL

061 02 02

062 65 ×

063 43 RCL

064 03 03

065 54 )

066 95 =

067 02 INV

068 39 cos  (arccos)

069 42 STO 

070 04 04

071 92 INV SBR


Examples


Calculating a:


Set the TI-58/TI-59 to Degrees mode:


Input:


50° [ A ]

45  [ B ]  (b)

35 [ C ] (c)

[ D ] returns a:  35.00312885


85° [ A ]

100  [ B ]  (b)

70 [ C ] (c)

[ D ] returns a:  116.9607609


Calculating θ:


52 [ A ]  (a)

38 [ B ] (b)

49 [ C ] (c)

[ E ] returns θ:  72.15813198


80 [ A ]  (a)

60 [ B ] (b)

65 [ C ] (c)

[ E ] returns θ:  79.47338145


Note:  The next post will be on July 23, 2022.


Eddie


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