trigonometric functions are part of mathematics beyond the elementary functions in the function of a class of functions. Their essence is a collection of arbitrary angle with a variable ratio between the collection of maps. The usual trigonometric functions in the Cartesian coordinate system is defined,replica jeans, its domain is the real number field. Another definition is in the right triangle, but not entirely. They described as a modern mathematical infinite series of limits and differential equations, to define extensions to the complex number system. Since the periodic trigonometric functions, it does not have a single-valued function of anti-sense function.

Applications trigonometric relationship between the value of the table the number of mathematical equations quotient relations tanα = sinα / cosα cotα = cosα / sinα square of the product compound of the plot difference formula and the formula three times the angle difference formula for sine two times the angle formula: twice the angle cosine formula: twice the angle of the tangent formula: Descending formula: applications in the complex trigonometric functions are more important in the application. In physics, trigonometry is also commonly used tools. It has six basic functions: sine cosine tangent function name secant cosecant cotangent symbol sin cos tan cot sec csc sine function sin (A) = a / c cosine function cos (A) = b / c tangent function tan (A ) = a / b cotangent functions cot (A) = b / a where A is a right side, b is the adjacent side, c is the hypotenuse trigonometric values ​​table sin0 = sin0 ° = 0 cos0 = cos0 ° = 1 tan0 = tan0 ° = 0 sin15 = 0.65028784015711686582974027098887; sin15 ° = (√ 6 - √ 2) / 4 cos15 =- 0.75968791285882127384814640363328; cos15 ° = (√ 6 + √ 2) / 4 tan15 =- 0.85599340090851876402619277823803; tan15 ° = 2 - √ 3 sin30 = -0.98803162409286178998774890729446; sin30 ° = 6 / 12 cos30 = 0.15425144988758405071866214661421; cos30 ° = √ 3 / 2 tan30 =- 6.405331196646275784896075505668; tan30 ° = √ 3 / 3 sin45 = 0.85090352453411842486237967761804; sin45 ° = √ 2 / 2 cos45 = 0.52532198881772969604746440482356; cos45 ° = sin45 ° = √ 2 / 2 tan45 = 1.6197751905438615499827965173949; tan45 ° = 1 sin60 =- 0.30481062110221670562564946547843; sin60 ° = √ 3 / 2 cos60 =- 0.95241298041515629269381659599293; cos60 ° = 6 / 12 tan60 = 0.32004038937956297493818761970571; tan60 ° = √ 3 sin75 =- 0.38778163540943043773094219282288; sin75 ° = cos15 ° cos75 = 0.92175126972474931639229684521414; cos75 ° = sin15 ° tan75 =- 0.42070095062112435384419621180484; tan75 ° = sin75 ° / cos75 ° = 2 + √ 3 sin90 = 0.89399666360055789051826949840421; sin90 ° = cos0 ° = 1 cos90 =- 0.44807361612917015236547731439964; cos90 ° = sin0 ° = 0 tan90 =- 1.9952004122082420252873530763796; tan90 ° does not exist sin105 =- 0.9705352835374847209338032056452; sin105 ° = cos15 ° cos105 =- 0.24095904923620141814219566395281; cos105 ° =- sin15 ° tan105 = 4.0278017638844193492341772197301; tan105 ° =- cot15 ° sin120 = 0.58061118421231428928240695979069 ; sin120 ° = cos30 ° cos120 = 0.81418097052656176790578986177889; cos120 ° =- sin30 ° tan120 = 0.71312300978590911614556745464875; tan120 ° =- tan60 ° sin135 = 0.088368686104001433036970666416798; sin135 ° = sin45 ° cos135 =- 0.99608783514118495835764440142782; cos135 ° =- cos45 ° tan135 =- 0.088715756770060446136984268003075 ; tan135 ° =- tan45 ° sin150 =- 0.71487642962916463143638609739663; sin150 ° = sin30 ° cos150 = 0.69925080647837513141645161882553; cos150 ° =- cos30 ° tan150 =- 1.0223462354365875649863661852619; tan150 ° =- tan30 ° sin165 = 0.99779727944989076515961268295525; sin165 ° = sin15 ° cos165 =- 0.066336936335623731837538732255201; cos165 ° =- cos15 ° tan165 =- 15.041353046538895371867886988769; tan165 ° =- tan15 ° sin180 =- 0.80115263573383047774673111582099; sin180 ° = sin0 ° = 0 cos180 =- 0.5984600690578581389679486481597; cos180 ° =- cos0 ° =- 1 tan180 = 1.3386902103511543616808987449579; tan180 ° = 0 sin195 = 0.21945466799406361597859718309894; sin195 ° =- sin15 ° cos195 = 0.97562269791944432311811100484535; cos195 ° =- cos15 ° tan195 = 0.22493805080802215296340937063051; tan195 ° = tan15 ° sin360 = 0.95891572341430650775887594775378; sin360 ° = sin0 ° = 0 cos360 =- 0.28369109148652733463742432444589; cos360 ° = cos0 ° = 1 tan360 =- 3.3801404139609579824775356112668; tan360 ° = tan0 ° = 0 cos72 = [(√ 5) -1] / 4 (using gold isosceles triangle can be drawn) sin1 = 0.01745240643728351 sin2 = 0.03489949670250097 sin3 = 0.05233595624294383 sin4 = 0.0697564737441253 sin5 = 0.08715574274765816 sin6 = 0.10452846326765346 sin7 = 0.12186934340514747 sin8 = 0.13917310096006544 sin9 = 0.15643446504023087 sin10 = 0.17364817766693033 sin11 = 0.1908089953765448 sin12 = 0.20791169081775931 sin13 = 0.22495105434386497 sin14 = 0.24192189559966773 sin15 = 0.25881904510252074 sin16 = 0.27563735581699916 sin17 = 0.2923717047227367 sin18 = 0.3090169943749474 sin19 = 0.3255681544571567 sin20 = 0.3420201433256687 sin21 = 0.35836794954530027 sin22 = 0.374606593415912 sin23 = 0.3907311284892737 sin24 = 0.40673664307580015 sin25 = 0.42261826174069944 sin26 = 0.4383711467890774 sin27 = 0.45399049973954675 sin28 = 0.4694715627858908 sin29 = 0.48480962024633706 sin30 = 0.49999999999999994 sin31 = 0.5150380749100542 sin32 = 0.5299192642332049 sin33 = 0.544639035015027 sin34 = 0.5591929034707468 sin35 = 0.573576436351046 sin36 = 0.5877852522924731 sin37 = 0.6018150231520483 sin38 = 0.6156614753256583 sin39 = 0.6293203910498375 sin40 = 0.6427876096865392 sin41 = 0.6560590289905073 sin42 = 0.6691306063588582 sin43 = 0.6819983600624985 sin44 = 0.6946583704589972 sin45 = 0.7071067811865475 sin46 = 0.7193398003386511 sin47 = 0.7313537016191705 sin48 = 0.7431448254773941 sin49 = 0.7547095802227719 sin50 = 0.766044443118978 sin51 = 0.7771459614569708 sin52 = 0.7880107536067219 sin53 = 0.7986355100472928 sin54 = 0.8090169943749474 sin55 = 0.8191520442889918 sin56 = 0.8290375725550417 sin57 = 0.8386705679454239 sin58 = 0.848048096156426 sin59 = 0.8571673007021122 sin60 = 0.8660254037844386 sin61 = 0.8746197071393957 sin62 = 0.8829475928589269 sin63 = 0.8910065241883678 sin64 = 0.898794046299167 sin65 = 0.9063077870366499 sin66 = 0.9135454576426009 sin67 = 0.9205048534524404 sin68 = 0.9271838545667873 sin69 = 0.9335804264972017 sin70 = 0.9396926207859083 sin71 = 0.9455185755993167 sin72 = 0.9510565162951535 sin73 = 0.9563047559630354 sin74 = 0.9612616959383189 sin75 = 0.9659258262890683 sin76 = 0.9702957262759965 sin77 = 0.9743700647852352 sin78 = 0.9781476007338057 sin79 = 0.981627183447664 sin80 = 0.984807753012208 sin81 = 0.9876883405951378 sin82 = 0.9902680687415704 sin83 = 0.992546151641322 sin84 = 0.9945218953682733 sin85 = 0.9961946980917455 sin86 = 0.9975640502598242 sin87 = 0.9986295347545738 sin88 = 0.9993908270190958 sin89 = 0.9998476951563913 sin90 = 1 cos1 = 0.9998476951563913 cos2 = 0.9993908270190958 cos3 = 0.9986295347545738 cos4 = 0.9975640502598242 cos5 = 0.9961946980917455 cos6 = 0.9945218953682733 cos7 = 0.992546151641322 cos8 = 0.9902680687415704 cos9 = 0.9876883405951378 cos10 = 0.984807753012208 cos11 = 0.981627183447664 cos12 = 0.9781476007338057 cos13 = 0.9743700647852352 cos14 = 0.9702957262759965 cos15 = 0.9659258262890683 cos16 = 0.9612616959383189 cos17 = 0.9563047559630355 cos18 = 0.9510565162951535 cos19 = 0.9455185755993168 cos20 = 0.9396926207859084 cos21 = 0.9335804264972017 cos22 = 0.9271838545667874 cos23 = 0.9205048534524404 cos24 = 0.9135454576426009 cos25 = 0.9063077870366499 cos26 = 0.898794046299167 cos27 = 0.8910065241883679 cos28 = 0.882947592858927 cos29 = 0.8746197071393957 cos30 = 0.8660254037844387 cos31 = 0.8571673007021123 cos32 = 0.848048096156426 cos33 = 0.838670567945424 cos34 = 0.8290375725550417 cos35 = 0.8191520442889918 cos36 = 0.8090169943749474 cos37 = 0.7986355100472928 cos38 = 0.7880107536067219 cos39 = 0.7771459614569709 cos40 = 0.766044443118978 cos41 = 0.754709580222772 cos42 = 0.7431448254773942 cos43 = 0.7313537016191705 cos44 = 0.7193398003386512 cos45 = 0.7071067811865476 cos46 = 0.6946583704589974 cos47 = 0.6819983600624985 cos48 = 0.6691306063588582 cos49 = 0.6560590289905074 cos50 = 0.6427876096865394 cos51 = 0.6293203910498375 cos52 = 0.6156614753256583 cos53 = 0.6018150231520484 cos54 = 0.5877852522924731 cos55 = 0.5735764363510462 cos56 = 0.5591929034707468 cos57 = 0.5446390350150272 cos58 = 0.5299192642332049 cos59 = 0.5150380749100544 cos60 = 0.5000000000000001 cos61 = 0.4848096202463371 cos62 = 0.46947156278589086 cos63 = 0.4539904997395468 cos64 = 0.43837114678907746 cos65 = 0.42261826174069944 cos66 = 0.4067366430758004 cos67 = 0.3907311284892737 cos68 = 0.3746065934159122 cos69 = 0.35836794954530015 cos70 = 0.3420201433256688 cos71 = 0.32556815445715675 cos72 = 0.30901699437494745 cos73 = 0.29237170472273677 cos74 = 0.27563735581699916 cos75 = 0.25881904510252074 cos76 = 0.24192189559966767 cos77 = 0.22495105434386514 cos78 = 0.20791169081775923 cos79 = 0.19080899537654491 cos80 = 0.17364817766693041 cos81 = 0.15643446504023092 cos82 = 0.13917310096006546 cos83 = 0.12186934340514749 cos84 = 0.10452846326765346 cos85 = 0.08715574274765836 cos86 = 0.06975647374412523 cos87 = 0.052335956242943966 cos88 = 0.03489949670250108 cos89 = 0.0174524064372836 cos90 = 0 tan1 = 0.017455064928217585 tan2 = 0.03492076949174773 tan3 = 0.052407779283041196 tan4 = 0.06992681194351041 tan5 = 0.08748866352592401 tan6 = 0.10510423526567646 tan7 = 0.1227845609029046 tan8 = 0.14054083470239145 tan9 = 0.15838444032453627 tan10 = 0.17632698070846497 tan11 = 0.19438030913771848 tan12 = 0.2125565616700221 tan13 = 0.2308681911255631 tan14 = 0.24932800284318068 tan15 = 0.2679491924311227 tan16 = 0.2867453857588079 tan17 = 0.30573068145866033 tan18 = 0.3249196962329063 tan19 = 0.34432761328966527 tan20 = 0.36397023426620234 tan21 = 0.3838640350354158 tan22 = 0.4040262258351568 tan23 = 0.4244748162096047 tan24 = 0.4452286853085361 tan25 = 0.4663076581549986 tan26 = 0.4877325885658614 tan27 = 0.5095254494944288 tan28 = 0.5317094316614788 tan29 = 0.554309051452769 tan30 = 0.5773502691896257 tan31 = 0.6008606190275604 tan32 = 0.6248693519093275 tan33 = 0.6494075931975104 tan34 = 0.6745085168424265 tan35 = 0.7002075382097097 tan36 = 0.7265425280053609 tan37 = 0.7535540501027942 tan38 = 0.7812856265067174 tan39 = 0.8097840331950072 tan40 = 0.8390996311772799 tan41 = 0.8692867378162267 tan42 = 0.9004040442978399 tan43 = 0.9325150861376618 tan44 = 0.9656887748070739 tan45 = 0.9999999999999999 tan46 = 1.0355303137905693 tan47 = 1.0723687100246826 tan48 = 1.1106125148291927 tan49 = 1.1503684072210092 tan50 = 1.19175359259421 tan51 = 1.234897156535051 tan52 = 1.2799416321930785 tan53 = 1.3270448216204098 tan54 = 1.3763819204711733 tan55 = 1.4281480067421144 tan56 = 1.4825609685127403 tan57 = 1.5398649638145827 tan58 = 1.6003345290410506 tan59 = 1.6642794823505173 tan60 = 1.7320508075688767 tan61 = 1.8040477552714235 tan62 = 1.8807264653463318 tan63 = 1.9626105055051503 tan64 = 2.050303841579296 tan65 = 2.1445069205095586 tan66 = 2.246036773904215 tan67 = 2.355852365823753 tan68 = 2.4750868534162946 tan69 = 2.6050890646938023 tan70 = 2.7474774194546216 tan71 = 2.904210877675822 tan72 = 3.0776835371752526 tan73 = 3.2708526184841404 tan74 = 3.4874144438409087 tan75 = 3.7320508075688776 tan76 = 4.0107809335358455 tan77 = 4.331475874284153 tan78 = 4.704630109478456 tan79 = 5.144554015970307 tan80 = 5.671281819617707 tan81 = 6.313751514675041 tan82 = 7.115369722384207 tan83 = 8.144346427974593 tan84 = 9.514364454222587 tan85 = 11.43005230276132 tan86 = 14.300666256711942 tan87 = 19.08113668772816 tan88 = 28.636253282915515 tan89 = 57.289961630759144 tan90 = no access relationship between the value of the number of mathematical equations tanα · cotα = 1 sinα · cscα = 1 cosα · secα = 1 quotient relations tanα = sinα / cosα cotα = cosα / sinα square of sinα ² + cosα ² = 1 1 + tanα & sup2; = secα ² 1 + cotα & sup2 = cscα ² the following relations,replica shoes, functions the same name,replica shoes, see the image quadrant. sin (2kπ + α) = sinα cos (2kπ + α) = cosα tan (2kπ + α ) = tanα cot (2kπ + α) = cotα sin (π + α) =- sinα cos (π + α) =- cosα tan (π + α) = tanα cot (π + α) = cotα sin (π-α ) = sinα cos (π-α) =- cosα tan (π-α) =- tanα cot (π-α) =- cotα sin (2π-α) =- sinα cos (2π-α) = cosα tan (2π -α) =- tanα cot (2π-α) =- cotα the following relationship,replica t-shirts, even the same odd change, to see symbol quadrant sin (90 °-α) = cosα cos (90 °-α) = sinα tan (90 ° - α) = cotα cot (90 °-α) = tanα sin (90 ° + α) = cosα cos (90 ° + α) =- sinα tan (90 ° + α) =- cotα cot (90 ° + α) = -tanα sin (270 °-α) =- cosα cos (270 °-α) =- sinα tan (270 °-α) = cotα cot (270 °-α) = tanα sin (270 ° + α) =- cosα cos (270 ° + α) = sinα tan (270 ° + α) =- cotα cot (270 ° + α) =- tanα product compounded difference formula sinα · cosβ = (1 / 2) * [sin (α + β) + sin (α-β)] cosα · sinβ = (1 / 2) * [sin (α + β)-sin (α-β)] cosα · cosβ = (1 / 2) * [cos (α + β) + cos (α-β)] sinα · sinβ = (1 / 2) * [cos (α + β)-cos (α-β)] and the difference of the quadrature formula sinα + sinβ = 2 * [sin (α + β ) / 2] * [cos (α-β) / 2] sinα-sinβ = 2 * [cos (α + β) / 2] * [sin (α-β) / 2] cosα + cosβ = 2 * [cos (α + β) / 2] * [cos (α-β) / 2] cosα-cosβ =- 22 * ​​[sin (α + β) / 2] * [sin (α-β) / 2] triple angle formula sin3α = 3sinα-4sinα ³ cos3α = 4cosα ³-3cosα corners and with the poor relationship between the trigonometric functions sin (α + β) = sinαcosβ + cosαsinβ sin (α-β) = sinαcosβ-cosαsinβ cos (α + β ) = cosαcosβ-sinαsinβ cos (α-β) = cosαcosβ + sinαsinβ tan (α + β) = (tanα + tanβ) / (1-tanα · tanβ) tan (α-β) = (tanα-tanβ) / (1 + tanα · tanβ) twice the angle of the sine formula: sin2α = 2cosαsinα derivation: sin2A = sin (A + A) = sinAcosA + cosAsinA = 2sinAcosA expansion formula: sin2A = 2sinAcosA = 2tanAcos ^ 2A = 2tanA / [1 + tan ^ 2A] 1 + sin2A = (sinA + cosA) ^ 2 times the angle cosine formula: twice the angle cosine formula representation of the three groups,replica handbags, three groups of forms equivalent: 1.Cos2a = Cos ^ 2a-Sin ^ 2a = [1-tan ^ 2a] / [1 + tan ^ 2a] 2.Cos2a = 1-2Sin ^ 2a 3.Cos2a = 2Cos ^ 2a-1 is derived: cos2A = cos (A + A) = cosAcosA-sinAsinA = cos ^ 2A-sin ^ 2A = 2cos ^ 2A-1 = 1-2sin ^ 2A twice the angle of the tangent formula: tan2α = 2tanα / [1-tan ^ 2α] is derived: tan2A = tan (A + A) = (tanA + tanA) / (1-tanAtanA) = 2tanA / [1-tan ^ 2A] descending formula: cosA ^ 2 = [1 + cos2A] / 2 sinA ^ 2 = [1-cos2A] / 2 tanA ^ 2 = [1-cos2A] / [1 + cos2A] variant : sin2α = sin ^ 2 (α + π / 4)-cos ^ 2 (α + π / 4) = 2sin ^ 2 (a + π / 4) -1 = 1-2cos ^ 2 (α + π / 4) ; cos2α = 2sin (α + π / 4) cos (α + π / 4) Further reading: 1

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