TIInterActive FileQCirkeltangenthldning Vi vil bestemme tangenthldningen i et fast punkt med 1. koordinat, x=k, p enhedscirklen ved at tilnrme med sekanter (som er linjer gennem to af cirklens punkter). Til sekantens andet variable fllespunkt med cirklen betegner vi 1. koordinaten x=t. Hvis det variable punkt, x=t, ligger langt fra det faste punkt, x=k, er tilnrmelsen ikke srlig god. Hvis det variable punkt, x=t, ligger tt ved det faste punkt, x=k - trk selv i skyderen nedenfor - kan du umiddelbart se, at tilnrmelsen bliver bedre. TI InterActive kan beregne grnsevrdien for alle disse tilnrmelsesvrdier, hvor t gr imod k - se nedenfor. Denne grnsevrdi er cirkeltangentens hldning i rringspunktet x=k. 1. tilnrmet med sekanthldninger Vi betragter enhedscirklen med ligning  P halvcirklen, som ligger over x-aksen, kan vi isolere y som funktion af x:  Vi sger hldningen for en cirkeltangent, som rrer cirklen i et fast punkt med 1. koordinat k.    Dette punkt har koordinater  Som tilnrmelse til tangenten betragter vi en sekant gennem det faste punkt og et andet, variabelt punkt  p cirklen.    Denne sekant har hldning  Tilnrmelsen er bedre, jo tttere x ligger ved k.  2. som grnsevrdi for sekanthldninger  K$ PP#P*PPNPcPdCP PPPPP[PHPXPYPZPkPoPP3PPP)P8PP"Verdana8"Verdana8"Verdana8"VerdanaxybcdeGHfgghoppqd p@ P !$`'r @dd;;.7. 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43 0 1ffff 4743000f 6870796c 72544f4d 656d6d69 9064 7800 6200 0 1ffff00 1000000 0 1000000 90800b00 78000000 62000000 0 ff000000 ff 100 0 19000300 2680 7800 6200 0 ffff00 1000000 0 20000000 448019 780000 620000 0 ffff0000 0 1 0 2680193d 78000000 62000000 0 ff000000 ff 100 0 2000 0 0 0 80270000 62 78 62 0 ffff 10000 0 10000 62800b 780000 620000 0 ffff0000 0 1 0 80190002 3c 78 62 0 1ffff 10000 0 19310000 2680 7800 6200 0 1ffff00 1000000 0 2e000000 0 0 1c0000 0 1801d 780000 ffff0000 ffff ffff0000 1 1 0 0 0 1c0000 1a 1a 1a 1a 0 0 0 0 0 1ffff 10000 0 0 0 10000 0 30000 43050000 5453454d 80000002 203d02 0(33 10001 0 0 2 0 13601 0 10000 0 0 0 0 0d@@(x)^(2) + (y)^(2)=1Verdana (x)^(2) + (y)^(2)=1.Verdana = |x0NANI!6]@ddh;"7" CTxobjItem"ࡱ>  Root EntryZn@3 @ContentsOlePres000 {ca7 64 64 1 1 1 0 ffff0007 b0002 796c4743 74536870 be656c79 ffffff 0 0 90000000 1 7010000 56000000 61647265 7700616e 6d6f5220 6e61 0 0 0 0 ff00ff00 6400ffff 64000000 8000000 6e617453 64726164 0 1 80010006 ffffff9c 0 0 0 190 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80000002 0 0617 64 64 1 1 1 0 ffff0007 b0002 796c4743 74536870 9c656c79 ffffff 0 0 90000000 1 7010000 56000000 61647265 7700616e 6d6f5220 6e61 0 0 0 ff000000 ff000000 6400ffff 64000000 8000000 6e617453 64726164 0 1 80010006 ffffff9c 0 0 0 190 1000000 7 626d7953 6c6f 0 0 0 0 0 0 ff ffffff 64 64 64745309 626d7953 16c6f 10000 0 8001 0 0 0 2bc0000 0 70100 79530000 6c6f626d 0 0 0 0 0 0 ff0000 ffff0000 6400ff 640000 530d0000 79536474 6c6f626d 646c6f42 1 1 80010000 0 0 0 0 190 1000001 7 656d6954 654e2073 6f522077 6e616d 0 0 0 0 ff ffffff 64 64 64745309 6c617449 16369 10000 0 8001 0 0 0 2bc0000 10000 70100 69540000 2073656d 2077654e 616d6f52 6e 0 0 0 ff0000 ffff0000 6400ff 640000 530d0000 74496474 63696c61 646c6f42 1 1 80010000 0 0 0 0 190 1000000 7 4d204954 687461 0 0 0 0 0 0 ff ffffff 64 64 64745305 14954 10000 0 8001 0 0 0 2bc0000 0 70100 49540000 74614d20 68 0 0 0 0 0 ff0000 ffff0000 6400ff 640000 53090000 49546474 646c6f42 1 1 30000 50004 70006 2cb0008 b40000 620000 0 0 0 1 0 1ffff 4743000a 6870796c 4854414d 1db 78 62 0 ffff 10000 0 10000 1ffff 4743000a 6870796c 574f524d 1db 78 62 0 ffff 10000 0 30000 1ffff 4743000b 6870796c 696c6544 4c6d 7800 6200 0 ffff00 1000000 0 1000000 4c800b00 78000000 62000000 0 ff000000 ff 100 0 ff000200 a0001ff 6c474300 43687079 35726168 78000000 62000000 0 1000000 100 100 0 80103d00 17 78 62 0 10001 10000 0 200000 0 0 1ffff00 43001400 70796c47 6d695368 43656c70 6f706d6f 726573 0 86000000 4000010 b ff000000 80001ff 6c474300 4d687079 18e4e 7800 6200 0 ffff00 1000000 0 1000000 8e800b00 78000001 62000000 0 ff000000 ff 100 0 10000700 2680 7800 6200 0 1ffff00 1000000 0 2e000000 3c8010 780000 620000 0 ffff0000 1 1 0 3c801038 78000000 62000000 0 ff000000 1ff 100 0 80103600 3c 78 62 0 1ffff 10000 0 10360000 3c80 7800 6200 0 1ffff00 1000000 0 30000000 3c8010 780000 620000 0 ffff0000 1 1 0 3c801032 78000000 62000000 0 ff000000 1ff 100 0 3500 0 0 14 ffff0000 a0001 796c4743 65546870 16d72 780000 ffff0000 ffff ffff0000 1 1 0 0 0 140000 9 9 9 9 0 2cb b4 ffffffff ffffffff 1ffff 10000 0 0 0 10000 0 30000 43050000 5453454d 80000002 1203d02 0(33 10001 0 0 2 0 13601 0 10000 0 0 0 0 0d@@f(k)Verdana .866025Verdana =  C  LLxz NANI`Jbz ,: X  H* ," bd xHTicBermuda SolidEurostar Black ExtendedEurostar BlackEurostar Regular ExtendedFalstaff Festival MTV:^@ddh;$7$ CTxobjItem$ࡱ>  Root EntryZn@3 @Contents~OlePres000_{ibed 64 64 1 1 1 0 ffff0007 b0002 796c4743 74536870 be656c79 ffffff 0 0 90000000 1 7010000 56000000 61647265 7700616e 6d6f5220 6e61 0 0 0 0 ff00ff00 6400ffff 64000000 8000000 6e617453 64726164 0 1 80010006 ffffff9c 0 0 0 190 1000000 7 626d7953 6c6f 0 0 0 0 0 0 ff0000 ffffff 64 64 64745309 626d7953 16c6f 10000 0 8001 0 0 0 2bc0000 0 70100 79530000 6c6f626d 0 0 0 0 0 0 0 ffff00ff 6400ff 640000 530d0000 79536474 6c6f626d 646c6f42 1 1 80010000 0 0 0 0 190 1000001 7 656d6954 654e2073 6f522077 6e616d 0 0 0 0 ff0000 ffffff 64 64 64745309 6c617449 16369 10000 0 8001 0 0 0 2bc0000 10000 70100 69540000 2073656d 2077654e 616d6f52 6e 0 0 0 0 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6c6f 0 0 0 0 0 0 ff ffffff 64 64 64745309 626d7953 16c6f 10000 0 8001 0 0 0 2bc0000 0 70100 79530000 6c6f626d 0 0 0 0 0 0 ff0000 ffff0000 6400ff 640000 530d0000 79536474 6c6f626d 646c6f42 1 1 80010000 0 0 0 0 190 1000001 7 656d6954 654e2073 6f522077 6e616d 0 0 0 0 ff ffffff 64 64 64745309 6c617449 16369 10000 0 8001 0 0 0 2bc0000 10000 70100 69540000 2073656d 2077654e 616d6f52 6e 0 0 0 ff0000 ffff0000 6400ff 640000 530d0000 74496474 63696c61 646c6f42 1 1 80010000 0 0 0 0 190 1000000 7 4d204954 687461 0 0 0 0 0 0 ff ffffff 64 64 64745305 14954 10000 0 8001 0 0 0 2bc0000 0 70100 49540000 74614d20 68 0 0 0 0 0 ff0000 ffff0000 6400ff 640000 53090000 49546474 646c6f42 1 1 30000 50004 70006 5540008 b40000 620000 0 0 0 1 0 1ffff 47430009 6870796c 646c6f43 78000004 62000000 0 ff000000 ff 100 0 ff000100 90001ff 6c474300 52687079 464776f 780000 620000 0 ffff0000 0 1 0 ffff0016 a0001 796c4743 68436870 3c7261 780000 620000 0 ffff0000 1 1 0 44800d45 78000000 62000000 0 ff000000 1ff 100 0 800d5600 44 78 62 0 1ffff 10000 0 d410000 3580 7800 6200 0 1ffff00 1000000 0 4c000000 26800d 780000 620000 0 ffff0000 1 1 0 3c800d20 78000000 62000000 0 ff000000 1ff 100 0 800d4500 3c 78 62 0 1ffff 10000 0 d520000 3c80 7800 6200 0 1ffff00 1000000 0 52000000 4b800d 780000 620000 0 ffff0000 1 1 0 3c800d4f 78000000 62000000 0 ff000000 1ff 100 0 800d5200 2d 78 62 0 1ffff 10000 0 d3a0000 2680 7800 6200 0 1ffff00 1000000 0 20000000 53800d 780000 620000 0 ffff0000 1 1 0 17800d4d 78000000 62000000 0 ff000000 1ff 100 0 800d6900 35 78 62 0 1ffff 10000 0 d730000 3580 7800 6200 0 1ffff00 1000000 0 73000000 17800d 780000 620000 0 ffff0000 1 1 0 3c800d69 78000000 62000000 0 ff000000 1ff 100 0 800d6e00 3c 78 62 0 1ffff 10000 0 d670000 2680 7800 6200 0 1ffff00 1000000 0 20000000 2d800d 780000 620000 0 ffff0000 1 1 0 1ffff29 43000a00 70796c47 72655468 16d 7800 ffffff00 ff 1ffff00 1000000 0 0 0 0 1ffff00 43001400 70796c47 6d695368 43656c70 6f706d6f 726573 0 58000000 50000011 1500000a 15000000 15000000 15000000 0 0 0 0 0 ff000000 1ff 100 0 0 0 100 0 300 4d430500 2545345 2800000 203d 30200000(33 10001 0 0 2 0 13601 0 10000 0 0 0 0 0d@@(t, sqrt(1 - (t)^(2)))Verdana EVAL ERROR: Missing )Verdana = NANI ? L-6 x Z[\]^fff"x8NT 08$@dd^ ; 7 CTxobjItem ࡱ> Root EntrynY$_rP%d!ContentsOlePres000 r(t1-10.010.1-0.38 Q??{Gz??/33 10001 0 0 2 0 13601 0 10000 0 0 0 0 1400000000NANI `$@dd8w;7 CTxobjItemࡱ>  Root EntryZn@3]!Contents\OlePres000:  !"#$%&'()*+,-./0123456789q 4aa 64 64 1 1 1 0 ffff0007 b0002 796c4743 74536870 9c656c79 ffffff 0 0 90000000 1 7010000 56000000 61647265 7700616e 6d6f5220 6e61 0 0 0 0 ff00ff00 6400ffff 64000000 8000000 6e617453 64726164 0 1 80010006 0 0 0 0 190 1000000 7 626d7953 6c6f 0 0 0 0 0 0 ff0000 ffffff 64 64 64745309 626d7953 16c6f 10000 0 8001 0 0 0 2bc0000 0 70100 79530000 6c6f626d 0 0 0 0 0 0 0 ffff00ff 6400ff 640000 530d0000 79536474 6c6f626d 646c6f42 1 1 80010000 0 0 0 0 190 1000001 7 656d6954 654e2073 6f522077 6e616d 0 0 0 0 ff0000 ffffff 64 64 64745309 6c617449 16369 10000 0 8001 0 0 0 2bc0000 10000 70100 69540000 2073656d 2077654e 616d6f52 6e 0 0 0 0 ffff00ff 6400ff 640000 530d0000 74496474 63696c61 646c6f42 1 1 80010000 0 0 0 0 190 1000000 7 4d204954 687461 0 0 0 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62000000 0 ff000000 ff 100 0 ff000200 a0001ff 6c474300 43687079 35726168 78000000 62000000 0 1000000 100 100 0 80103d00 17 78 62 0 10001 10000 0 200000 0 0 1ffff00 43001400 70796c47 6d695368 43656c70 6f706d6f 726573 0 23000000 c4000011 ffffff ff000000 80001ff 6c474300 4d687079 9e4e 7800 6200 0 ffff00 1000000 0 1000000 9e800b00 78000000 62000000 0 ff000000 ff 100 0 10000300 2680 7800 6200 0 1ffff00 1000000 0 2e000000 3c8010 780000 620000 0 ffff0000 1 1 0 3c801036 78000000 62000000 0 ff000000 1ff 100 0 3600 0 0 14 ffff0000 a0001 796c4743 65546870 16d72 780000 ffff0000 ffff ffff0000 1 1 0 0 0 140000 5 5 5 5 0 1db b4 ffffffff ffffffff 1ffff 10000 0 0 0 10000 0 30000 43050000 5453454d 80000002 1203d02 0(33 10001 0 0 2 0 13601 0 10000 0 0 0 0 0d@@tVerdana .66Verdana = 3 10001 0 0 2 0 13601 0 10000 0 0 0 NANI0 0d@@tVerdana -.38Verdana = S`$@dd5w;7 CTxobjItemࡱ>   Root EntryZn@3]! @ContentsOlePres000 695 64 64 1 1 1 0 ffff0007 b0002 796c4743 74536870 9c656c79 ffffff 0 0 90000000 1 7010000 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640000 53090000 49546474 646c6f42 1 1 30000 50004 70006 2cb0008 b40000 620000 0 0 0 1 0 1ffff 4743000a 6870796c 4854414d 1db 78 62 0 ffff 10000 0 10000 1ffff 4743000a 6870796c 574f524d 1db 78 62 0 ffff 10000 0 30000 1ffff 4743000b 6870796c 696c6544 4c6d 7800 6200 0 ffff00 1000000 0 1000000 4c800b00 78000000 62000000 0 ff000000 ff 100 0 ff000200 a0001ff 6c474300 43687079 35726168 78000000 62000000 0 1000000 100 100 0 80103d00 17 78 62 0 10001 10000 0 200000 0 0 1ffff00 43001400 70796c47 6d695368 43656c70 6f706d6f 726573 0 8d000000 c4000010 ffffff ff000000 80001ff 6c474300 4d687079 18e4e 7800 6200 0 ffff00 1000000 0 1000000 8e800b00 78000001 62000000 0 ff000000 ff 100 0 10000700 2680 7800 6200 0 1ffff00 1000000 0 2e000000 3c8010 780000 620000 0 ffff0000 1 1 0 3c801037 78000000 62000000 0 ff000000 1ff 100 0 80103500 3c 78 62 0 1ffff 10000 0 10310000 3c80 7800 6200 0 1ffff00 1000000 0 32000000 3c8010 780000 620000 0 ffff0000 1 1 0 3c801036 78000000 62000000 0 ff000000 1ff 100 0 3600 0 0 14 ffff0000 a0001 796c4743 65546870 16d72 780000 ffff0000 ffff ffff0000 1 1 0 0 0 140000 9 9 9 9 0 2cb b4 ffffffff ffffffff 1ffff 10000 0 0 0 10000 0 30000 43050000 5453454d 80000002 1203d02 0(33 10001 0 0 2 0 13601 0 10000 0 0 0 0 0d@@f(t)Verdana .751266Verdana = NANIU'@ddA ;070 CTxobjItem 0ࡱ>  Root EntryZn@3 @Contents $OlePres000r116c7 64 64 1 1 1 0 ffff0007 b0002 796c4743 74536870 be656c79 ffffff 0 0 90000000 1 7010000 56000000 61647265 7700616e 6d6f5220 6e61 0 0 0 0 ff00ff00 6400ffff 64000000 8000000 6e617453 64726164 0 1 80010006 ffffff9c 0 0 0 190 1000000 7 626d7953 6c6f 0 0 0 0 0 0 ff0000 ffffff 64 64 64745309 626d7953 16c6f 10000 0 8001 0 0 0 2bc0000 0 70100 79530000 6c6f626d 0 0 0 0 0 0 0 ffff00ff 6400ff 640000 530d0000 79536474 6c6f626d 646c6f42 1 1 80010000 0 0 0 0 190 1000001 7 656d6954 654e2073 6f522077 6e616d 0 0 0 0 ff0000 ffffff 64 64 64745309 6c617449 16369 10000 0 8001 0 0 0 2bc0000 10000 70100 69540000 2073656d 2077654e 616d6f52 6e 0 0 0 0 ffff00ff 6400ff 640000 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10000 0 10650000 2680 7800 6200 0 1ffff00 1000000 0 22000000 0 0 ffff0000 140001 796c4743 69536870 656c706d 706d6f43 7265736f 0 0 1158 9c1 0 1ffff 4743000a 6870796c 6d726554 1 78 ffffffff 0 1ffff 10000 0 0 0 0 60018 60000 60000 60000 0 0 0 0 0 ffff0000 1 1 0 0 0 1 0 3 454d4305 25453 3d028000 20 1ff00(33 10001 0 0 2 0 13601 0 10000 0 0 0 0 0d@@:a(t) := ( sqrt(1 - (t)^(2)) - sqrt(1 - (k)^(2)))/(t - k)Verdana "Done"Verdana = = C @[\]^fff"V&*NT`9f 9*1 Uxxp ]T ]4 ] *NANIAqln,@dd4w;.7. 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