Trigonometrisko funkciju grafiki:
sinuss,
kosinuss,
tangenss,
kotangenss,
sekanss,
kosekanss
Trigonometriska funkcija ir jebkura no funkcijām sin x, cos x, tg x, ctg x, sec x un cosec x, kur arguments x ir leņķis. Raksturīga šo funkciju īpašība ir to periodiskums.
Ne katra periodiska funkcija, kuras arguments ir leņķis, ir trigonometriska funkcija. Piemēram, funkcija
nav trigonometriska funkcija.
Vienības aplis ar kosinusa un sinusa vērtībām
Funkcija
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Apzīmējums
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Apraksts
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Sakarības (izmantojot radiānus)
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Sinuss
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sin
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Kosinuss
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cos
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Tangenss
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tg
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Kotangenss
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ctg
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Sekanss
|
sec
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Kosekanss
|
cosec (vai csc)
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|
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0° (0 rad) |
30° (π/6) |
45° (π/4) |
60° (π/3) |
90° (π/2) |
180° (π) |
270° (3π/2) |
360° (2π)
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, kur
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, kur
.
Tā kā sinuss un kosinuss ir attiecīgi punkta ordināta un abscisa, kas atbilst leņķa α riņķim, tad, atbilstoši Pitagora teorēmai

Dalot šīs vienādības abas puses ar sinusa kvadrātu vai kosinusa kvadrātu, iegūstam:


Sinuss un kosinuss ir nepārtrauktas funkcijas, bet tangensam, kotangensam, sekansam un kosekansam ir pārtraukuma punkti
kotangenss un kosekanss —
Kosinuss un sekanss ir funkcijas, kurām ir simetrija attiecībā uz funkcijas zīmes maiņu. Pārējām četrām funkcijām tādas īpašības nav, t.i.:






Funkcijas
,
,
un
ir periodiskas funkcijas ar periodu
. Savukārt, funkcijas
un
ir periodiskas ar periodu
Summas trigonometriskās funkcijas nozīme un divu leņķu starpība:




Līdzīgas formulas trim leņķiem:


Divkārša leņķa formulas:




Trīskārša leņķa formulas:




Citas leņķu daudzkārtņu formulas:








Pusleņķa formulas:






Formulas divu leņķu reizināšanai:






Līdzīgas formulas triju leņķu sinusu un kosinusu reizināšanai:




Attiecīgās formulas triju leņķu tangensiem un kotangensiem var iegūt, izdalot augstāk minēto vienādojumu labās puses ar kreisajām.
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Funkcijām ar argumentu
ir vienādojums:

kur leņķi
atrod pēc formulas:

Jebkuru trigonometrisko funkciju var izteikt kā pusleņķa tangensu.
θ grādos
|
θ radiānos
|
sin θ
|
cos θ
|
tan θ
|
0 |
0 |
0.0 |
1.0 |
0.0
|
1 |
0.017453293 |
0.01745240 |
0.9998477 |
0.017455065
|
2 |
0.034906585 |
0.034899497 |
0.99939083 |
0.034920769
|
3 |
0.052359878 |
0.052335956 |
0.99862953 |
0.052407779
|
4 |
0.06981317 |
0.069756474 |
0.99756405 |
0.069926812
|
5 |
0.087266463 |
0.087155743 |
0.9961947 |
0.087488664
|
6 |
0.10471976 |
0.10452846 |
0.9945219 |
0.10510424
|
7 |
0.12217305 |
0.12186934 |
0.99254615 |
0.12278456
|
8 |
0.13962634 |
0.1391731 |
0.99026807 |
0.14054083
|
9 |
0.15707963 |
0.15643447 |
0.98768834 |
0.15838444
|
10 |
0.17453293 |
0.17364818 |
0.98480775 |
0.17632698
|
11 |
0.19198622 |
0.190809 |
0.98162718 |
0.19438031
|
12 |
0.20943951 |
0.20791169 |
0.9781476 |
0.21255656
|
13 |
0.2268928 |
0.22495105 |
0.97437006 |
0.23086819
|
14 |
0.2443461 |
0.2419219 |
0.97029573 |
0.249328
|
15 |
0.26179939 |
0.25881905 |
0.96592583 |
0.26794919
|
16 |
0.27925268 |
0.27563736 |
0.9612617 |
0.28674539
|
17 |
0.29670597 |
0.2923717 |
0.95630476 |
0.30573068
|
18 |
0.31415927 |
0.30901699 |
0.95105652 |
0.3249197
|
19 |
0.33161256 |
0.32556815 |
0.94551858 |
0.34432761
|
20 |
0.34906585 |
0.34202014 |
0.93969262 |
0.36397023
|
21 |
0.36651914 |
0.35836795 |
0.93358043 |
0.38386404
|
22 |
0.38397244 |
0.37460659 |
0.92718385 |
0.40402623
|
23 |
0.40142573 |
0.39073113 |
0.92050485 |
0.42447482
|
24 |
0.41887902 |
0.40673664 |
0.91354546 |
0.44522869
|
25 |
0.43633231 |
0.42261826 |
0.90630779 |
0.46630766
|
26 |
0.45378561 |
0.43837115 |
0.89879405 |
0.48773259
|
27 |
0.4712389 |
0.4539905 |
0.89100652 |
0.50952545
|
28 |
0.48869219 |
0.46947156 |
0.88294759 |
0.53170943
|
29 |
0.50614548 |
0.48480962 |
0.87461971 |
0.55430905
|
30 |
0.52359878 |
0.5 |
0.8660254 |
0.57735027
|
31 |
0.54105207 |
0.51503807 |
0.8571673 |
0.60086062
|
32 |
0.55850536 |
0.52991926 |
0.8480481 |
0.62486935
|
33 |
0.57595865 |
0.54463904 |
0.83867057 |
0.64940759
|
34 |
0.59341195 |
0.5591929 |
0.82903757 |
0.67450852
|
35 |
0.61086524 |
0.57357644 |
0.81915204 |
0.70020754
|
36 |
0.62831853 |
0.58778525 |
0.80901699 |
0.72654253
|
37 |
0.64577182 |
0.60181502 |
0.79863551 |
0.75355405
|
38 |
0.66322512 |
0.61566148 |
0.78801075 |
0.78128563
|
39 |
0.68067841 |
0.62932039 |
0.77714596 |
0.80978403
|
40 |
0.6981317 |
0.64278761 |
0.76604444 |
0.83909963
|
41 |
0.71558499 |
0.65605903 |
0.75470958 |
0.86928674
|
42 |
0.73303829 |
0.66913061 |
0.74314483 |
0.90040404
|
43 |
0.75049158 |
0.68199836 |
0.7313537 |
0.93251509
|
44 |
0.76794487 |
0.69465837 |
0.7193398 |
0.96568877
|
45 |
0.78539816 |
0.70710678 |
0.70710678 |
1.0
|
46 |
0.80285146 |
0.7193398 |
0.69465837 |
1.03553031
|
47 |
0.82030475 |
0.7313537 |
0.68199836 |
1.07236871
|
48 |
0.83775804 |
0.74314483 |
0.66913061 |
1.11061251
|
49 |
0.85521133 |
0.75470958 |
0.65605903 |
1.15036841
|
50 |
0.87266463 |
0.76604444 |
0.64278761 |
1.19175359
|
51 |
0.89011792 |
0.77714596 |
0.62932039 |
1.23489716
|
52 |
0.90757121 |
0.78801075 |
0.61566148 |
1.27994163
|
53 |
0.9250245 |
0.79863551 |
0.60181502 |
1.32704482
|
54 |
0.9424778 |
0.80901699 |
0.58778525 |
1.37638192
|
55 |
0.95993109 |
0.81915204 |
0.57357644 |
1.42814801
|
56 |
0.97738438 |
0.82903757 |
0.5591929 |
1.48256097
|
57 |
0.99483767 |
0.83867057 |
0.54463904 |
1.53986496
|
58 |
1.01229097 |
0.8480481 |
0.52991926 |
1.60033453
|
59 |
1.02974426 |
0.8571673 |
0.51503807 |
1.66427948
|
60 |
1.04719755 |
0.8660254 |
0.5 |
1.73205081
|
61 |
1.06465084 |
0.87461971 |
0.48480962 |
1.80404776
|
62 |
1.08210414 |
0.88294759 |
0.46947156 |
1.88072647
|
63 |
1.09955743 |
0.89100652 |
0.4539905 |
1.96261051
|
64 |
1.11701072 |
0.89879405 |
0.43837115 |
2.05030384
|
65 |
1.13446401 |
0.90630779 |
0.42261826 |
2.14450692
|
66 |
1.15191731 |
0.91354546 |
0.40673664 |
2.24603677
|
67 |
1.1693706 |
0.92050485 |
0.39073113 |
2.35585237
|
68 |
1.18682389 |
0.92718385 |
0.37460659 |
2.47508685
|
69 |
1.20427718 |
0.93358043 |
0.35836795 |
2.60508906
|
70 |
1.22173048 |
0.93969262 |
0.34202014 |
2.74747742
|
71 |
1.23918377 |
0.94551858 |
0.32556815 |
2.90421088
|
72 |
1.25663706 |
0.95105652 |
0.30901699 |
3.07768354
|
73 |
1.27409035 |
0.95630476 |
0.2923717 |
3.27085262
|
74 |
1.29154365 |
0.9612617 |
0.27563736 |
3.48741444
|
75 |
1.30899694 |
0.96592583 |
0.25881905 |
3.73205081
|
76 |
1.32645023 |
0.97029573 |
0.2419219 |
4.01078093
|
77 |
1.34390352 |
0.97437006 |
0.22495105 |
4.33147587
|
78 |
1.36135682 |
0.9781476 |
0.20791169 |
4.70463011
|
79 |
1.37881011 |
0.98162718 |
0.190809 |
5.14455402
|
80 |
1.3962634 |
0.98480775 |
0.17364818 |
5.67128182
|
81 |
1.41371669 |
0.98768834 |
0.15643447 |
6.31375151
|
82 |
1.43116999 |
0.99026807 |
0.1391731 |
7.11536972
|
83 |
1.44862328 |
0.99254615 |
0.12186934 |
8.14434643
|
84 |
1.46607657 |
0.9945219 |
0.10452846 |
9.51436445
|
85 |
1.48352986 |
0.9961947 |
0.087155743 |
11.4300523
|
86 |
1.50098316 |
0.99756405 |
0.069756474 |
14.3006663
|
87 |
1.51843645 |
0.99862953 |
0.052335956 |
19.0811367
|
88 |
1.53588974 |
0.99939083 |
0.034899497 |
28.6362533
|
89 |
1.55334303 |
0.9998477 |
0.01745240 |
57.2899616
|
90 |
1.57079633 |
1.0 |
0.0 |
∞
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