程式3)三角形解 (Solution of triangle)
- 順著方向(順或逆時針),輸入三角形的三項資料(e.g., 角邊角) 【注:邊長加負號(見例3-1)】,
- 依序輸出三角形的六項資料(按輸入方向順序,邊角邊角.... 或 角邊角邊...)及其面積(全部共7項)
(注1:輸入的順序要如同證明全等三角形一樣, 順著一個方向入)
(注2:SAA三角形輸入次序,不能倒轉 [i.e., 不能改為AAS]; 否則會輸出錯誤答案)
(注3:ASS三角形, 若沒解,會出現答案異常[MATH ERROR])
(注4:若只知三角並按由小至大輸入,可以求得三邊的比例。[見例3-2])
(注5:若多於三個資料,可任意選取其中三個輸入。)
(注6:輸入的資料即使不能構成三角形(e.g., 三隻角總角度大於180°),仍可輸出答案,請小心核查輸入資料)
(注7:要在DEG Mode執行)
三角形解程式碼(197 bytes)
- (注: πr 按 [Shift][EXP][Shif][Ans][2] ; 90o 按 90[Shift][Ans][1])
- [入程式若遇困難,請看:計數機程式基本輸入技巧]
While 1: ?→A: ?→B: ?→C: 0>AB
=> Goto 0: B→X: - sin(C) ÷ sin(A→B:
(37 bytes)
0>A =>cos-1((A2+X2-C2)÷(2AX→B: X→C: Lbl 0: 0>C→D: Abs(A◢ (76 bytes)
Abs(B◢ 0>A => Break: D => πr - A - sin-1( C-1 Bsin(A→C: C◢ (103 bytes)
Pol( B tan(90o - A - C , -B ) sin(A◢ Y◢ X sin(C◢ - . 5AnsBsin(A◢ (134 bytes)
YD - A→C: Ans>0 => Goto 0: WhileEnd : cos-1( D => Asin(B+C) ÷ sin(C→C: (165 bytes)
- C◢ Pol(Ans + Acos(B , -Asin(B: Y◢ X◢ πr - B - Y◢ . 5ACsin(B (197 bytes)
例3-1:已知三邊求三角形解
a=4, b=5, c=6,求∠A、∠B、∠C及三角形面積。
- 按Prog [3],再按 -4 EXE -5 EXE -6
按EXE (顯示a) |
|
按EXE (顯示∠C) |
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjamu61X2Pcez2QBbgse3JZyE3rz-SKQqy-MqKmPPrFOn9SWKvnfe6NDEOjUf3pVDo6J8NlneS8Ojl_h8RSGbaKX4Fmct0M9IgoIX6lJDc_q1_iN7W9tc5ndcGTJ14b5zCgYp3I/s400/Program3-2.jpg) |
按EXE (顯示b) |
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKD98hPgpdtqjwnR504mE_LZLNuJtP89jtCe2RSuMxqCgmGHmkmOkCAldKOc5CKJu8JEiWBKksqymrHginhk6JO6kS3YoYL8M5v5pTy3msNHrpGLGBlcXsFqhO6p7cY5sZjTrb/s400/Program3-3.jpg) |
按EXE (顯示∠A) |
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAXP8RhVB8Cj9ZyUxXnPnzbtbreDESP-3rq1J0p5zSfWwvI8HwqzkIGfcjabVlJh9JDRmb4zmGTBeqPmnk1CVNQhCyw12DGJQlxgtlWaRJ_dNj6v88xUlYcvUBzEhj5r-2JyHQ/s400/Program3-4.jpg) |
按EXE (顯示c) |
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_TVqkYD4quCZ8HxTgnJO8ovcDpKDcA49dbF6gvoQgD7GcUl0vG_8c2n6HXxeKn-aO_framAtQUBXC3FMty4mq2VV9mbQw7jAebr3t0pJhAQia80x3L-XR-fmc-iMXNcOyEvtr/s400/Program3-5.jpg) |
按EXE (顯示∠B) |
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoLncLMpliD8NfrCwEQY67IulUPuMFnFP8vtEkddSHNn7YKTZiS3suc25uabDwi9_YX46BmW3bVviv_2IQVyAAXRAuJaL_sxrji1C6na5Y0qh8BxCOvhfM1Q-Hx9qIfVGEh4wE/s400/Program3-6.jpg) |
按EXE (顯示面積) |
|
例3-2:已知三角形的三隻角求三邊長比例
∠A = 40o, ∠B = 60o, ∠C = 80°,求三邊的比例。
- (先輸入最小的角,使邊長皆大於1 )
- 按Prog [3],再按 40 EXE 60 EXE 80
按EXE (顯示∠A) |
![DSE數學計算機程式3](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgG7SitO-RgKCJoBtttk3w_F8DkFlllbpahFj1baGWxNU8AIsRAofG9TUd7XnWC8P8nM5U4FdHIf7D4wgKYl2_8S2DEeaSG6FKkvO16jHk5vVnhdNLLLk-9B6_1gvdx47bNr0092g/s1600/Program3_2.jpg+%25281%2529.jpg) |
按EXE (顯示c) |
![DSE數學計算機程式3](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-gJuuSH4HmN1UCwyvqjm0GCK63jqhv9UqDFKq39jg06PBZHeZtUW4FQRVQeDdQkv4Y43gDSWNtWBBQga3WxKbSXDdYxoxsXDGXmK85fTVfkMPSoLFvqQrrkThwHvYEycpo_SXmA/s1600/Program3_2.jpg+%25282%2529.jpg) |
按EXE (顯示∠B) |
![DSE數學計算機程式3](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggIh-rUF5Dtkh6Ma_oXQxzH4Je8pGx4POpznxLmIsXJqYysCpWw_dN180swDxN2SAc2VHJzd4bbkhde_oGjojQ26TAEfJGSgbr5B_Al4oIIiw6ILvTWAlV17KvlKmJe_MCZEwMjw/s1600/Program3_2.jpg+%25283%2529.jpg) |
按EXE (顯示a) |
![DSE數學計算機程式3](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_IK2E4FuZDj6W9N1ozd343Py7eFpnxiapcSIyH8KFQxpqD-PCZAjbxU2LZaM2XFM1L4SqEQPDgH7tN-QX1KgmhdIp_uXLVloHRGJjNmpsczLuyNVIHcBKgYqqeb7lZr_8236YQA/s1600/Program3_2.jpg+%25284%2529.jpg) |
按EXE (顯示∠C) |
![DSE數學計算機程式3](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCj8FlLIGt4lGN9m28POobYt2tt5tiXXW_boAlxyKXkThbzcF60w8rqgu7n7BxXV5RUOQq6KSqIvGKfascmXevJh_XBpykZCVH_nrda7VpBI6B67mij0a9eotZIBDxGdgIav-ZrQ/s1600/Program3_2.jpg+%25285%2529.jpg) |
按EXE (顯示b) |
![DSE數學計算機程式3](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZOOjxEs85y4Yzgv4p5V2yTbXeOxU5PbjojT5WPkf1FVNS9SEQCO1lMdH801BWruaZv_lFGO_QsS61FhVcdVoeUE45jMtaXEI1Mn2x2sOmQFlC36lxhhgKM64MSGhWKOHjZFMhfw/s1600/Program3_2.jpg+%25286%2529.jpg) |
按EXE (顯示面積) |
![DSE數學計算機程式3](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMiMtcUqsprRUGRaSN7UOGAT2iwoFTUqTA-bE216iEbDJ0u-hjXkudFbw1CqD4XrDFu2Dn2nxnPS_XZcWPSWFbAdkRoSTPHhF0mrfNC3RW3mQwH2yQImFDBDgq13HY_NZhgggg0Q/s1600/Program3_2.jpg+%25287%2529.jpg) |
答案:a : b : c = 1: 1.3473 : 1.5321
程式4)四次(或以下)方程解 (Quartic Equations)
- 輸入 Ax4+ Bx3+ Cx2+ Dx + E = 0中的A,B,C,D,E (5 項)
- 輸出最多四個解
(注1:若要解三次方程問題,把 E 輸入為 0,(即把整條方程乘以 x) 並忽略 0 的解,見例 4-2)
(注2:輸出答案時,畫面右上方若顯示"Re<=>Im",則表示該解非實解[unreal root],見例 4-2)
(注3:計算完畢後,按[Mode][1]轉回普通計算模式(COMP))
四次方程解程式碼(221 bytes)
- 程式需要在 CMPLX 模式下執行,因此在選擇新程式位置後,按 2 選用CMPLX模式。
- (注: 5!o 按 [5][SHIFT][x-1][SHIFT][Ans][1] ; πr 按 [Shift][EXP][Shift][Ans][2])
- [入程式若遇困難,請先看:計數機程式基本輸入技巧]
?→A: ?→B: ?→C: ?→D: ?→M: B┘(4A→B: C┘A - 6B2→C: (38 bytes)
D┘A - 4B3 - 2BC→D: M┘A - B( B3 + BC + D→M: C2 - 4M→X: (76 bytes)
8C3 - 9┘2( 2CX+3D2→Y: 4C2 - 3X→M: √( Y2 - M3: Ans - Y - 2Ans( Ans=Y→Y: (123 bytes)
3√( Abs( Ans => Ans∠( 3-1arg( Y ) + 5!o (πr = arg( Y→Y: Abs(Ans => Y + M┘Y: (157 bytes)
√( ( Ans - 2C)┘3→A: √( X→X: A => D┘A→X: For -1→D to 1 Step 2: √( 2DX - 2C-A2→M: (205 bytes)
( M - DA )┘2 - B◢ Ans - M◢ Next (221 bytes)
例4-1: 4次方程求解(全實根)
解2x4 - 11x3 - 12x2 + 71x + 70 = 0
- 按 Prog [4],再按 2 EXE - 11 EXE - 12 EXE 71 EXE 70
按EXE (顯示第一個根) |
![DSE數學計算機程式4](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXTE1Mo8NBNE6yn8kftvmLp6AKpjUD4noDRHm97gsLiFZz5fevjNCtFVks5chxA64CDm0o6jGlygoTrwYz3hvM5b12Mqk_6uCLt4Wka0I9ibIAzGu9gUwJDWX0TGbLMJWcjcTvKg/s1600/Program4+%25281%2529.jpg) |
按EXE (顯示第二個根) |
![DSE數學計算機程式4](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfOPV6g-HXPLG1ZizN0C2ulVbusKeuDIXsNm38jQHABH5P2hcCJGcJPODAyLSj2c-rODTOGUQebw0DqWCkok2_nhm8nXaw6gB9zCFwWAsnDFOqRVkpg8enhY6wLsc0hBqHmmqJnA/s1600/Program4+%25282%2529.jpg) |
按EXE (顯示第三個根) |
![DSE數學計算機程式4](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeWvXu5CjAvnYKTXS-UTv69BLc8lQ43iUS7HVuh0j0-8ZAcpH012cUleSx7NwxWni3q7R8eTKWMejH5q2jsEtMpHm-ZK5ZlY3LuJ6O_B2wFozIIk5ASstajPIpHKfEoDejEWvtAA/s1600/Program4+%25283%2529.jpg) |
按EXE (顯示第四個根) |
![DSE數學計算機程式4](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHk6CB7fBSjsr21zwYeOHBS7Q_eCNA7Agm6W1Y8PfmspdICMsfwU4WTUygv-XWAHchoQuUZ4O1lAM-dcuDc82CBmbFHS58qEN40MnrNdgVJFqnAU0rsuTq8tD_bXzUTKVsLRVGGQ/s1600/Program4+%25284%2529.jpg) |
按EXE (顯示Next,計算完結) |
![DSE數學計算機程式4](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWkCZmTd_cLnSZj6jv9NUV0qHGX3vOvZcAEXyMnV7hpRA-dBujCEEqgs0NvudnripWVbHKTkVEH8ulyegEPKPGy6buigNNja0jIm6E1TznWcMQtHKHkBrKhKRNR117YQxeKlMFWg/s1600/Program4+%25285%2529.jpg) |
按AC 終止程式
之後計數機會繼續在Cplx mode,按需要變回普通計算模式(COMP)
例4-2: 4次方程求解(部分非實根)
解 3x3 - 5x2 + x - 4 =0
- 3次方的問題,要當作4次方輸入:3x4 - 5x3 + x2 - 4x =0 (會多了一個x=0的答案)
- 按 Prog [4],再按 3 EXE - 5 EXE 1 EXE - 4 EXE 0 EXE
按EXE (顯示第一個根) |
![DSE數學計算機程式4](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9IdmraHDXsfgLtlx9iO8QfNf_D12qJn1JViELCulIOAdy_TR2rEGwgKFEEKCG2sOwNe3dqygbzkD9A2CRGsrh8BrLDgNVkyajVRznctPS6AZxVUeoRKK0TvYrbCrHvSsOdXlLzQ/s1600/Program4_2+%25281%2529.jpg) |
按EXE (顯示第二個根,非答案) |
![DSE數學計算機程式4](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjadwyuhuQNQzqJRRcZr34EB5DtxagbkWcJcDlc4-G3LiHVkmuFkk8PpOoV5gFXkHL6HOC4_BVdl0IRAXYTEZuBvlPEirYpWcwAO8kmH9SAfP7YCEZnH3e9Rkg_97fSPOO33gf98Q/s1600/Program4_2+%25282%2529.jpg) |
按EXE (顯示第三個根實數部) |
![DSE數學計算機程式4](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxKFuRftOiwvjggBzM3uVbR7ZDJ_L4J4ROQ57k85ZQ-gNVAGMnrTaiI1gyymy2i1XqzhqFY_nkG1LEjMjZBJ2ARtMqK_LrjWwsZpfnrOQa3iqp7K4O5aFGoPQTAXlBfV5SCGP4KA/s1600/Program4_2+%25283%2529.jpg) |
按Shift Re<=>Im (顯示第三個根虛數部) |
|
按EXE (顯示第四個根的實數部) |
![DSE數學計算機程式4](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAgJ70tI2Fuj8PQFupVXTu5hL4AOMpt3sMq_WPbJDIGJDSe4yd4nuNquRlJr-VbOD8go23SKUNMOYoTqsXTAXQFODjvYSlwjvbo-GRYyMt9MVDelNlEnuOT6hW4bRKZfnPzlSpdg/s1600/Program4_2+%25285%2529.jpg) |
按Shift Re<=>Im (顯示第四個根虛數部) |
![DSE數學計算機程式4](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVkj7WQ3DcBKir_0RDL0x1za37tNBKuMqg-ZyJrHp8az5W90VTN1mU4Q_IwGtFIHKD2I9CMjgbXvdvAB68bO4tP3BrUs3Rp-s5Hlx3X-L2Y2g48Lx5kPsUKuFQ8JoRyOfXKBrOvA/s1600/Program4_2+%25286%2529.jpg) |
按EXE (顯示Next,計算完結) |
![DSE數學計算機程式4](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmtpkMdGhWOnwto588XEtNO66vKgiMDKbGQcYsHYR2WoPv-3h-AwbovK4kdPShyoerK0wsg48QLLGhLKBVKynsSxHWJhjLoFPaAqNuKlOzG1rylcINpSXlVtVu87uvG2LSS6CEtw/s1600/Program4_2+%25287%2529.jpg) |
按AC 終止程式
之後計數機會繼續在Cplx mode,按需要變回普通計算模式(COMP)
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