Home » Archimedes archive » Archimedes World » AW-1996-07.adf » !Ignotum_Ignotum » !Ignotum/Formulae/Trig
!Ignotum/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.
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| Tape/disk: | Home » Archimedes archive » Archimedes World » AW-1996-07.adf » !Ignotum_Ignotum |
| Filename: | !Ignotum/Formulae/Trig |
| Read OK: | ✔ |
| File size: | 04B9 bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
# Maths > Trig. Identities 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 63 6f 74 78 3d |Identities.cotx=| 00000020 31 2f 74 61 6e 78 0a 43 6f 74 78 20 69 73 20 61 |1/tanx.Cotx is a| 00000030 20 66 75 6e 63 74 69 6f 6e 20 6f 66 20 78 20 65 | function of x e| 00000040 71 75 61 6c 20 74 6f 20 74 68 65 0a 72 65 63 69 |qual to the.reci| 00000050 70 72 6f 63 61 6c 20 6f 66 20 74 61 6e 78 2e 0a |procal of tanx..| 00000060 0a 0a 0a 63 6f 73 65 63 78 3d 31 2f 73 69 6e 78 |...cosecx=1/sinx| 00000070 0a 43 6f 73 65 63 78 20 69 73 20 61 20 66 75 6e |.Cosecx is a fun| 00000080 63 74 69 6f 6e 20 6f 66 20 78 20 65 71 75 61 6c |ction of x equal| 00000090 20 74 6f 20 74 68 65 0a 72 65 63 69 70 72 6f 63 | to the.reciproc| 000000a0 61 6c 20 6f 66 20 73 69 6e 78 2e 0a 0a 0a 0a 73 |al of sinx.....s| 000000b0 65 63 78 3d 31 2f 63 6f 73 78 0a 53 65 63 78 20 |ecx=1/cosx.Secx | 000000c0 69 73 20 61 20 66 75 6e 63 74 69 6f 6e 20 6f 66 |is a function of| 000000d0 20 78 20 65 71 75 61 6c 20 74 6f 20 74 68 65 0a | x equal to the.| 000000e0 72 65 63 69 70 72 6f 63 61 6c 20 6f 66 20 63 6f |reciprocal of co| 000000f0 73 78 2e 0a 0a 0a 0a 73 69 6e b2 78 2b 63 6f 73 |sx.....sin.x+cos| 00000100 b2 78 3d 31 0a 41 20 63 6f 6d 6d 6f 6e 6c 79 20 |.x=1.A commonly | 00000110 75 73 65 64 20 69 64 65 6e 74 69 74 79 2c 20 75 |used identity, u| 00000120 73 65 64 20 74 6f 20 6f 62 74 61 69 6e 0a 6d 61 |sed to obtain.ma| 00000130 6e 79 20 6f 66 20 74 68 65 20 6d 6f 72 65 20 63 |ny of the more c| 00000140 6f 6d 70 6c 65 78 20 69 64 65 6e 74 69 74 69 65 |omplex identitie| 00000150 73 2e 0a 4e 6f 74 65 3a 20 73 69 6e b2 78 3d 28 |s..Note: sin.x=(| 00000160 73 69 6e 78 29 b2 0a 0a 0a 63 6f 74 b2 78 2b 31 |sinx)....cot.x+1| 00000170 3d 63 6f 73 65 63 b2 78 0a 0a 0a 0a 0a 0a 74 61 |=cosec.x......ta| 00000180 6e b2 78 2b 31 3d 73 65 63 b2 78 0a 0a 0a 0a 0a |n.x+1=sec.x.....| 00000190 0a 63 6f 73 b2 78 3d bd 28 31 2b 63 6f 73 32 78 |.cos.x=.(1+cos2x| 000001a0 29 0a 0a 0a 0a 0a 0a 73 69 6e b2 78 3d bd 28 31 |)......sin.x=.(1| 000001b0 2d 63 6f 73 32 78 29 0a 0a 0a 0a 0a 0a 73 69 6e |-cos2x)......sin| 000001c0 32 78 3d 32 73 69 6e 78 63 6f 73 78 0a 0a 0a 0a |2x=2sinxcosx....| 000001d0 0a 0a 63 6f 73 32 78 3d 31 2d 32 73 69 6e b2 78 |..cos2x=1-2sin.x| 000001e0 0a 0a 0a 0a 0a 0a 63 6f 73 32 78 3d 32 63 6f 73 |......cos2x=2cos| 000001f0 b2 78 2d 31 0a 0a 0a 0a 0a 0a 63 6f 73 32 78 3d |.x-1......cos2x=| 00000200 63 6f 73 b2 78 2d 73 69 6e b2 78 0a 0a 0a 0a 0a |cos.x-sin.x.....| 00000210 0a 74 61 6e 32 78 3d 28 32 74 61 6e 78 29 2f 28 |.tan2x=(2tanx)/(| 00000220 31 2d 74 61 6e b2 78 29 0a 0a 0a 0a 0a 0a 73 69 |1-tan.x)......si| 00000230 6e 28 41 2b 42 29 3d 73 69 6e 41 63 6f 73 42 2b |n(A+B)=sinAcosB+| 00000240 63 6f 73 41 73 69 6e 42 0a 57 68 65 72 65 20 41 |cosAsinB.Where A| 00000250 20 61 6e 64 20 42 20 61 72 65 20 62 6f 74 68 20 | and B are both | 00000260 61 6e 67 6c 65 73 2e 0a 0a 0a 0a 0a 73 69 6e 28 |angles......sin(| 00000270 41 2d 42 29 3d 73 69 6e 41 63 6f 73 42 2d 63 6f |A-B)=sinAcosB-co| 00000280 73 41 73 69 6e 42 0a 57 68 65 72 65 20 41 20 61 |sAsinB.Where A a| 00000290 6e 64 20 42 20 61 72 65 20 62 6f 74 68 20 61 6e |nd B are both an| 000002a0 67 6c 65 73 2e 0a 0a 0a 0a 0a 63 6f 73 28 41 2b |gles......cos(A+| 000002b0 42 29 3d 63 6f 73 41 63 6f 73 42 2d 73 69 6e 41 |B)=cosAcosB-sinA| 000002c0 73 69 6e 42 0a 57 68 65 72 65 20 41 20 61 6e 64 |sinB.Where A and| 000002d0 20 42 20 61 72 65 20 62 6f 74 68 20 61 6e 67 6c | B are both angl| 000002e0 65 73 2e 0a 0a 0a 0a 0a 63 6f 73 28 41 2d 42 29 |es......cos(A-B)| 000002f0 3d 63 6f 73 41 63 6f 73 42 2b 73 69 6e 41 73 69 |=cosAcosB+sinAsi| 00000300 6e 42 0a 57 68 65 72 65 20 41 20 61 6e 64 20 42 |nB.Where A and B| 00000310 20 61 72 65 20 62 6f 74 68 20 61 6e 67 6c 65 73 | are both angles| 00000320 2e 0a 0a 0a 0a 0a 74 61 6e 28 41 2b 42 29 3d 28 |......tan(A+B)=(| 00000330 74 61 6e 41 2b 74 61 6e 42 29 2f 28 31 2d 74 61 |tanA+tanB)/(1-ta| 00000340 6e 41 74 61 6e 42 29 0a 57 68 65 72 65 20 41 20 |nAtanB).Where A | 00000350 61 6e 64 20 42 20 61 72 65 20 62 6f 74 68 20 61 |and B are both a| 00000360 6e 67 6c 65 73 2e 0a 0a 0a 0a 0a 74 61 6e 28 41 |ngles......tan(A| 00000370 2d 42 29 3d 28 74 61 6e 41 2d 74 61 6e 42 29 2f |-B)=(tanA-tanB)/| 00000380 28 31 2b 74 61 6e 41 74 61 6e 42 29 0a 57 68 65 |(1+tanAtanB).Whe| 00000390 72 65 20 41 20 61 6e 64 20 42 20 61 72 65 20 62 |re A and B are b| 000003a0 6f 74 68 20 61 6e 67 6c 65 73 2e 0a 0a 0a 0a 0a |oth angles......| 000003b0 32 73 69 6e 41 63 6f 73 42 3d 73 69 6e 28 41 2b |2sinAcosB=sin(A+| 000003c0 42 29 2b 73 69 6e 28 41 2d 42 29 0a 57 68 65 72 |B)+sin(A-B).Wher| 000003d0 65 20 41 20 61 6e 64 20 42 20 61 72 65 20 62 6f |e A and B are bo| 000003e0 74 68 20 61 6e 67 6c 65 73 2e 0a 0a 0a 0a 0a 32 |th angles......2| 000003f0 63 6f 73 41 73 69 6e 42 3d 73 69 6e 28 41 2b 42 |cosAsinB=sin(A+B| 00000400 29 2d 73 69 6e 28 41 2d 42 29 0a 57 68 65 72 65 |)-sin(A-B).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 32 63 |h angles......2c| 00000430 6f 73 41 63 6f 73 42 3d 63 6f 73 28 41 2b 42 29 |osAcosB=cos(A+B)| 00000440 2b 63 6f 73 28 41 2d 42 29 0a 57 68 65 72 65 20 |+cos(A-B).Where | 00000450 41 20 61 6e 64 20 42 20 61 72 65 20 62 6f 74 68 |A and B are both| 00000460 20 61 6e 67 6c 65 73 2e 0a 0a 0a 0a 0a 2d 32 73 | angles......-2s| 00000470 69 6e 41 73 69 6e 42 3d 63 6f 73 28 41 2d 42 29 |inAsinB=cos(A-B)| 00000480 2d 63 6f 73 28 41 2d 42 29 0a 57 68 65 72 65 20 |-cos(A-B).Where | 00000490 41 20 61 6e 64 20 42 20 61 72 65 20 62 6f 74 68 |A and B are both| 000004a0 20 61 6e 67 6c 65 73 2e 0a 0a 0a 0a 0a 0a 0a 0a | angles.........| 000004b0 0a 0a 0a 0a 0a 0a 0a 0a 0a |.........| 000004b9
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