Home » Archimedes archive » Acorn User » AU 1997-01 B.adf » Regulars » StarInfo/Allen/!Ignotum/Formulae/Formulae/Trig
StarInfo/Allen/!Ignotum/Formulae/Formulae/Trig
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Acorn User » AU 1997-01 B.adf » Regulars |
| Filename: | StarInfo/Allen/!Ignotum/Formulae/Formulae/Trig |
| Read OK: | ✔ |
| File size: | 063D bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
# Maths > Trig. Identities # New entries should take the form of: # Formula # Note 1 # Note 2 # Note 3 # Note 4 # Note 5 # Formula # Note 1 # And so on... # To fit snugly into the window, each line should be no longer # than 42 characters. # There is a limit of 25 formulas per topic. # Any notes should be made here, at the beginning and should # be preceeded by a hash (#). cotx=1/tanx Cotx is a function of x equal to the reciprocal of tanx. cosecx=1/sinx Cosecx is a function of x equal to the reciprocal of sinx. secx=1/cosx Secx is a function of x equal to the reciprocal of cosx. sin�x+cos�x=1 A commonly used identity, used to obtain many of the more complex identities. Note: sin�x=(sinx)� cot�x+1=cosec�x tan�x+1=sec�x cos�x=�(1+cos2x) sin�x=�(1-cos2x) sin2x=2sinxcosx cos2x=1-2sin�x cos2x=2cos�x-1 cos2x=cos�x-sin�x tan2x=(2tanx)/(1-tan�x) sin(A+B)=sinAcosB+cosAsinB Where A and B are both angles. sin(A-B)=sinAcosB-cosAsinB Where A and B are both angles. cos(A+B)=cosAcosB-sinAsinB Where A and B are both angles. cos(A-B)=cosAcosB+sinAsinB Where A and B are both angles. tan(A+B)=(tanA+tanB)/(1-tanAtanB) Where A and B are both angles. tan(A-B)=(tanA-tanB)/(1+tanAtanB) Where A and B are both angles. 2sinAcosB=sin(A+B)+sin(A-B) Where A and B are both angles. 2cosAsinB=sin(A+B)-sin(A-B) Where A and B are both angles. 2cosAcosB=cos(A+B)+cos(A-B) Where A and B are both angles. -2sinAsinB=cos(A-B)-cos(A-B) Where A and B are both angles.
00000000 23 20 4d 61 74 68 73 20 3e 20 54 72 69 67 2e 20 |# Maths > Trig. | 00000010 49 64 65 6e 74 69 74 69 65 73 0a 0a 23 20 4e 65 |Identities..# Ne| 00000020 77 20 65 6e 74 72 69 65 73 20 73 68 6f 75 6c 64 |w entries should| 00000030 20 74 61 6b 65 20 74 68 65 20 66 6f 72 6d 20 6f | take the form o| 00000040 66 3a 0a 23 20 20 20 20 20 46 6f 72 6d 75 6c 61 |f:.# Formula| 00000050 0a 23 20 20 20 20 20 4e 6f 74 65 20 31 0a 23 20 |.# Note 1.# | 00000060 20 20 20 20 4e 6f 74 65 20 32 0a 23 20 20 20 20 | Note 2.# | 00000070 20 4e 6f 74 65 20 33 0a 23 20 20 20 20 20 4e 6f | Note 3.# No| 00000080 74 65 20 34 0a 23 20 20 20 20 20 4e 6f 74 65 20 |te 4.# Note | 00000090 35 0a 23 20 20 20 20 20 46 6f 72 6d 75 6c 61 0a |5.# Formula.| 000000a0 23 20 20 20 20 20 4e 6f 74 65 20 31 0a 23 20 20 |# Note 1.# | 000000b0 20 20 20 41 6e 64 20 73 6f 20 6f 6e 2e 2e 2e 0a | And so on....| 000000c0 23 20 54 6f 20 66 69 74 20 73 6e 75 67 6c 79 20 |# To fit snugly | 000000d0 69 6e 74 6f 20 74 68 65 20 77 69 6e 64 6f 77 2c |into the window,| 000000e0 20 65 61 63 68 20 6c 69 6e 65 20 73 68 6f 75 6c | each line shoul| 000000f0 64 20 62 65 20 6e 6f 20 6c 6f 6e 67 65 72 0a 23 |d be no longer.#| 00000100 20 74 68 61 6e 20 34 32 20 63 68 61 72 61 63 74 | than 42 charact| 00000110 65 72 73 2e 0a 23 20 54 68 65 72 65 20 69 73 20 |ers..# There is | 00000120 61 20 6c 69 6d 69 74 20 6f 66 20 32 35 20 66 6f |a limit of 25 fo| 00000130 72 6d 75 6c 61 73 20 70 65 72 20 74 6f 70 69 63 |rmulas per topic| 00000140 2e 0a 0a 23 20 41 6e 79 20 6e 6f 74 65 73 20 73 |...# Any notes s| 00000150 68 6f 75 6c 64 20 62 65 20 6d 61 64 65 20 68 65 |hould be made he| 00000160 72 65 2c 20 61 74 20 74 68 65 20 62 65 67 69 6e |re, at the begin| 00000170 6e 69 6e 67 20 61 6e 64 20 73 68 6f 75 6c 64 0a |ning and should.| 00000180 23 20 62 65 20 70 72 65 63 65 65 64 65 64 20 62 |# be preceeded b| 00000190 79 20 61 20 68 61 73 68 20 28 23 29 2e 0a 0a 63 |y a hash (#)...c| 000001a0 6f 74 78 3d 31 2f 74 61 6e 78 0a 43 6f 74 78 20 |otx=1/tanx.Cotx | 000001b0 69 73 20 61 20 66 75 6e 63 74 69 6f 6e 20 6f 66 |is a function of| 000001c0 20 78 20 65 71 75 61 6c 20 74 6f 20 74 68 65 0a | x equal to the.| 000001d0 72 65 63 69 70 72 6f 63 61 6c 20 6f 66 20 74 61 |reciprocal of ta| 000001e0 6e 78 2e 0a 0a 0a 0a 63 6f 73 65 63 78 3d 31 2f |nx.....cosecx=1/| 000001f0 73 69 6e 78 0a 43 6f 73 65 63 78 20 69 73 20 61 |sinx.Cosecx is a| 00000200 20 66 75 6e 63 74 69 6f 6e 20 6f 66 20 78 20 65 | function of x e| 00000210 71 75 61 6c 20 74 6f 20 74 68 65 0a 72 65 63 69 |qual to the.reci| 00000220 70 72 6f 63 61 6c 20 6f 66 20 73 69 6e 78 2e 0a |procal of sinx..| 00000230 0a 0a 0a 73 65 63 78 3d 31 2f 63 6f 73 78 0a 53 |...secx=1/cosx.S| 00000240 65 63 78 20 69 73 20 61 20 66 75 6e 63 74 69 6f |ecx is a functio| 00000250 6e 20 6f 66 20 78 20 65 71 75 61 6c 20 74 6f 20 |n of x equal to | 00000260 74 68 65 0a 72 65 63 69 70 72 6f 63 61 6c 20 6f |the.reciprocal o| 00000270 66 20 63 6f 73 78 2e 0a 0a 0a 0a 73 69 6e b2 78 |f cosx.....sin.x| 00000280 2b 63 6f 73 b2 78 3d 31 0a 41 20 63 6f 6d 6d 6f |+cos.x=1.A commo| 00000290 6e 6c 79 20 75 73 65 64 20 69 64 65 6e 74 69 74 |nly used identit| 000002a0 79 2c 20 75 73 65 64 20 74 6f 20 6f 62 74 61 69 |y, used to obtai| 000002b0 6e 0a 6d 61 6e 79 20 6f 66 20 74 68 65 20 6d 6f |n.many of the mo| 000002c0 72 65 20 63 6f 6d 70 6c 65 78 20 69 64 65 6e 74 |re complex ident| 000002d0 69 74 69 65 73 2e 0a 4e 6f 74 65 3a 20 73 69 6e |ities..Note: sin| 000002e0 b2 78 3d 28 73 69 6e 78 29 b2 0a 0a 0a 63 6f 74 |.x=(sinx)....cot| 000002f0 b2 78 2b 31 3d 63 6f 73 65 63 b2 78 0a 0a 0a 0a |.x+1=cosec.x....| 00000300 0a 0a 74 61 6e b2 78 2b 31 3d 73 65 63 b2 78 0a |..tan.x+1=sec.x.| 00000310 0a 0a 0a 0a 0a 63 6f 73 b2 78 3d bd 28 31 2b 63 |.....cos.x=.(1+c| 00000320 6f 73 32 78 29 0a 0a 0a 0a 0a 0a 73 69 6e b2 78 |os2x)......sin.x| 00000330 3d bd 28 31 2d 63 6f 73 32 78 29 0a 0a 0a 0a 0a |=.(1-cos2x).....| 00000340 0a 73 69 6e 32 78 3d 32 73 69 6e 78 63 6f 73 78 |.sin2x=2sinxcosx| 00000350 0a 0a 0a 0a 0a 0a 63 6f 73 32 78 3d 31 2d 32 73 |......cos2x=1-2s| 00000360 69 6e b2 78 0a 0a 0a 0a 0a 0a 63 6f 73 32 78 3d |in.x......cos2x=| 00000370 32 63 6f 73 b2 78 2d 31 0a 0a 0a 0a 0a 0a 63 6f |2cos.x-1......co| 00000380 73 32 78 3d 63 6f 73 b2 78 2d 73 69 6e b2 78 0a |s2x=cos.x-sin.x.| 00000390 0a 0a 0a 0a 0a 74 61 6e 32 78 3d 28 32 74 61 6e |.....tan2x=(2tan| 000003a0 78 29 2f 28 31 2d 74 61 6e b2 78 29 0a 0a 0a 0a |x)/(1-tan.x)....| 000003b0 0a 0a 73 69 6e 28 41 2b 42 29 3d 73 69 6e 41 63 |..sin(A+B)=sinAc| 000003c0 6f 73 42 2b 63 6f 73 41 73 69 6e 42 0a 57 68 65 |osB+cosAsinB.Whe| 000003d0 72 65 20 41 20 61 6e 64 20 42 20 61 72 65 20 62 |re A and B are b| 000003e0 6f 74 68 20 61 6e 67 6c 65 73 2e 0a 0a 0a 0a 0a |oth angles......| 000003f0 73 69 6e 28 41 2d 42 29 3d 73 69 6e 41 63 6f 73 |sin(A-B)=sinAcos| 00000400 42 2d 63 6f 73 41 73 69 6e 42 0a 57 68 65 72 65 |B-cosAsinB.Where| 00000410 20 41 20 61 6e 64 20 42 20 61 72 65 20 62 6f 74 | A and B are bot| 00000420 68 20 61 6e 67 6c 65 73 2e 0a 0a 0a 0a 0a 63 6f |h angles......co| 00000430 73 28 41 2b 42 29 3d 63 6f 73 41 63 6f 73 42 2d |s(A+B)=cosAcosB-| 00000440 73 69 6e 41 73 69 6e 42 0a 57 68 65 72 65 20 41 |sinAsinB.Where A| 00000450 20 61 6e 64 20 42 20 61 72 65 20 62 6f 74 68 20 | and B are both | 00000460 61 6e 67 6c 65 73 2e 0a 0a 0a 0a 0a 63 6f 73 28 |angles......cos(| 00000470 41 2d 42 29 3d 63 6f 73 41 63 6f 73 42 2b 73 69 |A-B)=cosAcosB+si| 00000480 6e 41 73 69 6e 42 0a 57 68 65 72 65 20 41 20 61 |nAsinB.Where A a| 00000490 6e 64 20 42 20 61 72 65 20 62 6f 74 68 20 61 6e |nd B are both an| 000004a0 67 6c 65 73 2e 0a 0a 0a 0a 0a 74 61 6e 28 41 2b |gles......tan(A+| 000004b0 42 29 3d 28 74 61 6e 41 2b 74 61 6e 42 29 2f 28 |B)=(tanA+tanB)/(| 000004c0 31 2d 74 61 6e 41 74 61 6e 42 29 0a 57 68 65 72 |1-tanAtanB).Wher| 000004d0 65 20 41 20 61 6e 64 20 42 20 61 72 65 20 62 6f |e A and B are bo| 000004e0 74 68 20 61 6e 67 6c 65 73 2e 0a 0a 0a 0a 0a 74 |th angles......t| 000004f0 61 6e 28 41 2d 42 29 3d 28 74 61 6e 41 2d 74 61 |an(A-B)=(tanA-ta| 00000500 6e 42 29 2f 28 31 2b 74 61 6e 41 74 61 6e 42 29 |nB)/(1+tanAtanB)| 00000510 0a 57 68 65 72 65 20 41 20 61 6e 64 20 42 20 61 |.Where A and B a| 00000520 72 65 20 62 6f 74 68 20 61 6e 67 6c 65 73 2e 0a |re both angles..| 00000530 0a 0a 0a 0a 32 73 69 6e 41 63 6f 73 42 3d 73 69 |....2sinAcosB=si| 00000540 6e 28 41 2b 42 29 2b 73 69 6e 28 41 2d 42 29 0a |n(A+B)+sin(A-B).| 00000550 57 68 65 72 65 20 41 20 61 6e 64 20 42 20 61 72 |Where A and B ar| 00000560 65 20 62 6f 74 68 20 61 6e 67 6c 65 73 2e 0a 0a |e both angles...| 00000570 0a 0a 0a 32 63 6f 73 41 73 69 6e 42 3d 73 69 6e |...2cosAsinB=sin| 00000580 28 41 2b 42 29 2d 73 69 6e 28 41 2d 42 29 0a 57 |(A+B)-sin(A-B).W| 00000590 68 65 72 65 20 41 20 61 6e 64 20 42 20 61 72 65 |here A and B are| 000005a0 20 62 6f 74 68 20 61 6e 67 6c 65 73 2e 0a 0a 0a | both angles....| 000005b0 0a 0a 32 63 6f 73 41 63 6f 73 42 3d 63 6f 73 28 |..2cosAcosB=cos(| 000005c0 41 2b 42 29 2b 63 6f 73 28 41 2d 42 29 0a 57 68 |A+B)+cos(A-B).Wh| 000005d0 65 72 65 20 41 20 61 6e 64 20 42 20 61 72 65 20 |ere A and B are | 000005e0 62 6f 74 68 20 61 6e 67 6c 65 73 2e 0a 0a 0a 0a |both angles.....| 000005f0 0a 2d 32 73 69 6e 41 73 69 6e 42 3d 63 6f 73 28 |.-2sinAsinB=cos(| 00000600 41 2d 42 29 2d 63 6f 73 28 41 2d 42 29 0a 57 68 |A-B)-cos(A-B).Wh| 00000610 65 72 65 20 41 20 61 6e 64 20 42 20 61 72 65 20 |ere A and B are | 00000620 62 6f 74 68 20 61 6e 67 6c 65 73 2e 0a 0a 0a 0a |both angles.....| 00000630 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |.............| 0000063d
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