\n\n| 1<\/td>\n | 0.01745240643728351<\/td>\n<\/tr>\n |
\n| 2<\/td>\n | 0.03489949670250097<\/td>\n<\/tr>\n |
\n| 3<\/td>\n | 0.05233595624294383<\/td>\n<\/tr>\n |
\n| 4<\/td>\n | 0.0697564737441253<\/td>\n<\/tr>\n |
\n| 5<\/td>\n | 0.08715574274765816<\/td>\n<\/tr>\n |
\n| 6<\/td>\n | 0.10452846326765346<\/td>\n<\/tr>\n |
\n| 7<\/td>\n | 0.12186934340514747<\/td>\n<\/tr>\n |
\n| 8<\/td>\n | 0.13917310096006544<\/td>\n<\/tr>\n |
\n| 9<\/td>\n | 0.15643446504023087<\/td>\n<\/tr>\n |
\n| 10<\/td>\n | 0.17364817766693033<\/td>\n<\/tr>\n |
\n| 11<\/td>\n | 0.1908089953765448<\/td>\n<\/tr>\n |
\n| 12<\/td>\n | 0.20791169081775931<\/td>\n<\/tr>\n |
\n| 13<\/td>\n | 0.22495105434386497<\/td>\n<\/tr>\n |
\n| 14<\/td>\n | 0.24192189559966773<\/td>\n<\/tr>\n |
\n| 15<\/td>\n | 0.25881904510252074<\/td>\n<\/tr>\n |
\n| 16<\/td>\n | 0.27563735581699916<\/td>\n<\/tr>\n |
\n| 17<\/td>\n | 0.2923717047227367<\/td>\n<\/tr>\n |
\n| 18<\/td>\n | 0.3090169943749474<\/td>\n<\/tr>\n |
\n| 19<\/td>\n | 0.3255681544571567<\/td>\n<\/tr>\n |
\n| 20<\/td>\n | 0.3420201433256687<\/td>\n<\/tr>\n |
\n| 21<\/td>\n | 0.35836794954530027<\/td>\n<\/tr>\n |
\n| 22<\/td>\n | 0.374606593415912<\/td>\n<\/tr>\n |
\n| 23<\/td>\n | 0.3907311284892737<\/td>\n<\/tr>\n |
\n| 24<\/td>\n | 0.40673664307580015<\/td>\n<\/tr>\n |
\n| 25<\/td>\n | 0.42261826174069944<\/td>\n<\/tr>\n |
\n| 26<\/td>\n | 0.4383711467890774<\/td>\n<\/tr>\n |
\n| 27<\/td>\n | 0.45399049973954675<\/td>\n<\/tr>\n |
\n| 28<\/td>\n | 0.4694715627858908<\/td>\n<\/tr>\n |
\n| 29<\/td>\n | 0.48480962024633706<\/td>\n<\/tr>\n |
\n| 30<\/td>\n | 0.49999999999999994<\/td>\n<\/tr>\n |
\n| 31<\/td>\n | 0.5150380749100542<\/td>\n<\/tr>\n |
\n| 32<\/td>\n | 0.5299192642332049<\/td>\n<\/tr>\n |
\n| 33<\/td>\n | 0.544639035015027<\/td>\n<\/tr>\n |
\n| 34<\/td>\n | 0.5591929034707468<\/td>\n<\/tr>\n |
\n| 35<\/td>\n | 0.573576436351046<\/td>\n<\/tr>\n |
\n| 36<\/td>\n | 0.5877852522924731<\/td>\n<\/tr>\n |
\n| 37<\/td>\n | 0.6018150231520483<\/td>\n<\/tr>\n |
\n| 38<\/td>\n | 0.6156614753256583<\/td>\n<\/tr>\n |
\n| 39<\/td>\n | 0.6293203910498375<\/td>\n<\/tr>\n |
\n| 40<\/td>\n | 0.6427876096865392<\/td>\n<\/tr>\n |
\n| 41<\/td>\n | 0.6560590289905073<\/td>\n<\/tr>\n |
\n| 42<\/td>\n | 0.6691306063588582<\/td>\n<\/tr>\n |
\n| 43<\/td>\n | 0.6819983600624985<\/td>\n<\/tr>\n |
\n| 44<\/td>\n | 0.6946583704589972<\/td>\n<\/tr>\n |
\n| 45<\/td>\n | 0.7071067811865475<\/td>\n<\/tr>\n |
\n| 46<\/td>\n | 0.7193398003386511<\/td>\n<\/tr>\n |
\n| 47<\/td>\n | 0.7313537016191705<\/td>\n<\/tr>\n |
\n| 48<\/td>\n | 0.7431448254773941<\/td>\n<\/tr>\n |
\n| 49<\/td>\n | 0.7547095802227719<\/td>\n<\/tr>\n |
\n| 50<\/td>\n | 0.766044443118978<\/td>\n<\/tr>\n |
\n| 51<\/td>\n | 0.7771459614569708<\/td>\n<\/tr>\n |
\n| 52<\/td>\n | 0.7880107536067219<\/td>\n<\/tr>\n |
\n| 53<\/td>\n | 0.7986355100472928<\/td>\n<\/tr>\n |
\n| 54<\/td>\n | 0.8090169943749474<\/td>\n<\/tr>\n |
\n| 55<\/td>\n | 0.8191520442889918<\/td>\n<\/tr>\n |
\n| 56<\/td>\n | 0.8290375725550417<\/td>\n<\/tr>\n |
\n| 57<\/td>\n | 0.8386705679454239<\/td>\n<\/tr>\n |
\n| 58<\/td>\n | 0.848048096156426<\/td>\n<\/tr>\n |
\n| 59<\/td>\n | 0.8571673007021122<\/td>\n<\/tr>\n |
\n| 60<\/td>\n | 0.8660254037844386<\/td>\n<\/tr>\n |
\n| 61<\/td>\n | 0.8746197071393957<\/td>\n<\/tr>\n |
\n| 62<\/td>\n | 0.8829475928589269<\/td>\n<\/tr>\n |
\n| 63<\/td>\n | 0.8910065241883678<\/td>\n<\/tr>\n |
\n| 64<\/td>\n | 0.898794046299167<\/td>\n<\/tr>\n |
\n| 65<\/td>\n | 0.9063077870366499<\/td>\n<\/tr>\n |
\n| 66<\/td>\n | 0.9135454576426009<\/td>\n<\/tr>\n |
\n| 67<\/td>\n | 0.9205048534524404<\/td>\n<\/tr>\n |
\n| 68<\/td>\n | 0.9271838545667873<\/td>\n<\/tr>\n |
\n| 69<\/td>\n | 0.9335804264972017<\/td>\n<\/tr>\n |
\n| 70<\/td>\n | 0.9396926207859083<\/td>\n<\/tr>\n |
\n| 71<\/td>\n | 0.9455185755993167<\/td>\n<\/tr>\n |
\n| 72<\/td>\n | 0.9510565162951535<\/td>\n<\/tr>\n |
\n| 73<\/td>\n | 0.9563047559630354<\/td>\n<\/tr>\n |
\n| 74<\/td>\n | 0.9612616959383189<\/td>\n<\/tr>\n |
\n| 75<\/td>\n | 0.9659258262890683<\/td>\n<\/tr>\n |
\n| 76<\/td>\n | 0.9702957262759965<\/td>\n<\/tr>\n |
\n| 77<\/td>\n | 0.9743700647852352<\/td>\n<\/tr>\n |
\n| 78<\/td>\n | 0.9781476007338057<\/td>\n<\/tr>\n |
\n| 79<\/td>\n | 0.981627183447664<\/td>\n<\/tr>\n |
\n| 80<\/td>\n | 0.984807753012208<\/td>\n<\/tr>\n |
\n| 81<\/td>\n | 0.9876883405951378<\/td>\n<\/tr>\n |
\n| 82<\/td>\n | 0.9902680687415704<\/td>\n<\/tr>\n |
\n| 83<\/td>\n | 0.992546151641322<\/td>\n<\/tr>\n |
\n| 84<\/td>\n | 0.9945218953682733<\/td>\n<\/tr>\n |
\n| 85<\/td>\n | 0.9961946980917455<\/td>\n<\/tr>\n |
\n| 86<\/td>\n | 0.9975640502598242<\/td>\n<\/tr>\n |
\n| 87<\/td>\n | 0.9986295347545738<\/td>\n<\/tr>\n |
\n| 88<\/td>\n | 0.9993908270190958<\/td>\n<\/tr>\n |
\n| 89<\/td>\n | 0.9998476951563913<\/td>\n<\/tr>\n |
\n| 90<\/td>\n | 1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n Warto\u015bci te s\u0105 obliczane za pomoc\u0105 standardowych bibliotek matematycznych, co zapewnia precyzj\u0119. Na przyk\u0142ad sin(30\u00b0) \u2248 0,5, co jest warto\u015bci\u0105 idealn\u0105 do oblicze\u0144 tr\u00f3jk\u0105t\u00f3w 30-60-90 w projektowaniu przek\u0142adni.<\/p>\n Tabela funkcji cosinus<\/h2>\nCosinus to stosunek d\u0142ugo\u015bci przyprostok\u0105tnej do przeciwprostok\u0105tnej, malej\u0105cy od 1 przy 0\u00b0 do 0 przy 90\u00b0. Jest on kluczowy dla oblicze\u0144 sk\u0142adowych poziomych wektor\u00f3w si\u0142 lub ruchu pocisku w uk\u0142adach mechanicznych.<\/p>\n \n \n\n\n| K\u0105t (\u00b0)<\/th>\n | warto\u015b\u0107 cos<\/th>\n<\/tr>\n<\/thead>\n | \n\n| 1<\/td>\n | 0.9998476951563913<\/td>\n<\/tr>\n | \n| 2<\/td>\n | 0.9993908270190958<\/td>\n<\/tr>\n | \n| 3<\/td>\n | 0.9986295347545738<\/td>\n<\/tr>\n | \n| 4<\/td>\n | 0.9975640502598242<\/td>\n<\/tr>\n | \n| 5<\/td>\n | 0.9961946980917455<\/td>\n<\/tr>\n | \n| 6<\/td>\n | 0.9945218953682733<\/td>\n<\/tr>\n | \n| 7<\/td>\n | 0.992546151641322<\/td>\n<\/tr>\n | \n| 8<\/td>\n | 0.9902680687415704<\/td>\n<\/tr>\n | \n| 9<\/td>\n | 0.9876883405951378<\/td>\n<\/tr>\n | \n| 10<\/td>\n | 0.984807753012208<\/td>\n<\/tr>\n | \n| 11<\/td>\n | 0.981627183447664<\/td>\n<\/tr>\n | \n| 12<\/td>\n | 0.9781476007338057<\/td>\n<\/tr>\n | \n| 13<\/td>\n | 0.9743700647852352<\/td>\n<\/tr>\n | \n| 14<\/td>\n | 0.9702957262759965<\/td>\n<\/tr>\n | \n| 15<\/td>\n | 0.9659258262890683<\/td>\n<\/tr>\n | \n| 16<\/td>\n | 0.9612616959383189<\/td>\n<\/tr>\n | \n| 17<\/td>\n | 0.9563047559630355<\/td>\n<\/tr>\n | \n| 18<\/td>\n | 0.9510565162951535<\/td>\n<\/tr>\n | \n| 19<\/td>\n | 0.9455185755993168<\/td>\n<\/tr>\n | \n| 20<\/td>\n | 0.9396926207859084<\/td>\n<\/tr>\n | \n| 21<\/td>\n | 0.9335804264972017<\/td>\n<\/tr>\n | \n| 22<\/td>\n | 0.9271838545667874<\/td>\n<\/tr>\n | \n| 23<\/td>\n | 0.9205048534524404<\/td>\n<\/tr>\n | \n| 24<\/td>\n | 0.9135454576426009<\/td>\n<\/tr>\n | \n| 25<\/td>\n | 0.9063077870366499<\/td>\n<\/tr>\n | \n| 26<\/td>\n | 0.898794046299167<\/td>\n<\/tr>\n | \n| 27<\/td>\n | 0.8910065241883679<\/td>\n<\/tr>\n | \n| 28<\/td>\n | 0.882947592858927<\/td>\n<\/tr>\n | \n| 29<\/td>\n | 0.8746197071393957<\/td>\n<\/tr>\n | \n| 30<\/td>\n | 0.8660254037844387<\/td>\n<\/tr>\n | \n| 31<\/td>\n | 0.8571673007021123<\/td>\n<\/tr>\n | \n| 32<\/td>\n | 0.848048096156426<\/td>\n<\/tr>\n | \n| 33<\/td>\n | 0.838670567945424<\/td>\n<\/tr>\n | \n| 34<\/td>\n | 0.8290375725550417<\/td>\n<\/tr>\n | \n| 35<\/td>\n | 0.8191520442889918<\/td>\n<\/tr>\n | \n| 36<\/td>\n | 0.8090169943749474<\/td>\n<\/tr>\n | \n| 37<\/td>\n | 0.7986355100472928<\/td>\n<\/tr>\n | \n| 38<\/td>\n | 0.7880107536067219<\/td>\n<\/tr>\n | \n| 39<\/td>\n | 0.7771459614569709<\/td>\n<\/tr>\n | \n| 40<\/td>\n | 0.766044443118978<\/td>\n<\/tr>\n | \n| 41<\/td>\n | 0.754709580222772<\/td>\n<\/tr>\n | \n| 42<\/td>\n | 0.7431448254773942<\/td>\n<\/tr>\n | \n| 43<\/td>\n | 0.7313537016191705<\/td>\n<\/tr>\n | \n| 44<\/td>\n | 0.7193398003386512<\/td>\n<\/tr>\n | \n| 45<\/td>\n | 0.7071067811865476<\/td>\n<\/tr>\n | \n| 46<\/td>\n | 0.6946583704589974<\/td>\n<\/tr>\n | \n| 47<\/td>\n | 0.6819983600624985<\/td>\n<\/tr>\n | \n| 48<\/td>\n | 0.6691306063588582<\/td>\n<\/tr>\n | \n| 49<\/td>\n | 0.6560590289905074<\/td>\n<\/tr>\n | \n| 50<\/td>\n | 0.6427876096865394<\/td>\n<\/tr>\n | \n| 51<\/td>\n | 0.6293203910498375<\/td>\n<\/tr>\n | \n| 52<\/td>\n | 0.6156614753256583<\/td>\n<\/tr>\n | \n| 53<\/td>\n | 0.6018150231520484<\/td>\n<\/tr>\n | \n| 54<\/td>\n | 0.5877852522924731<\/td>\n<\/tr>\n | \n| 55<\/td>\n | 0.5735764363510462<\/td>\n<\/tr>\n | \n| 56<\/td>\n | 0.5591929034707468<\/td>\n<\/tr>\n | \n| 57<\/td>\n | 0.5446390350150272<\/td>\n<\/tr>\n | \n| 58<\/td>\n | 0.5299192642332049<\/td>\n<\/tr>\n | \n| 59<\/td>\n | 0.5150380749100544<\/td>\n<\/tr>\n | \n| 60<\/td>\n | 0.5000000000000001<\/td>\n<\/tr>\n | \n| 61<\/td>\n | 0.4848096202463371<\/td>\n<\/tr>\n | \n| 62<\/td>\n | 0.46947156278589086<\/td>\n<\/tr>\n | \n| 63<\/td>\n | 0.4539904997395468<\/td>\n<\/tr>\n | \n| 64<\/td>\n | 0.43837114678907746<\/td>\n<\/tr>\n | \n| 65<\/td>\n | 0.42261826174069944<\/td>\n<\/tr>\n | \n| 66<\/td>\n | 0.4067366430758004<\/td>\n<\/tr>\n | \n| 67<\/td>\n | 0.3907311284892737<\/td>\n<\/tr>\n | \n| 68<\/td>\n | 0.3746065934159122<\/td>\n<\/tr>\n | \n| 69<\/td>\n | 0.35836794954530015<\/td>\n<\/tr>\n | \n| 70<\/td>\n | 0.3420201433256688<\/td>\n<\/tr>\n | \n| 71<\/td>\n | 0.32556815445715675<\/td>\n<\/tr>\n | \n| 72<\/td>\n | 0.30901699437494745<\/td>\n<\/tr>\n | \n| 73<\/td>\n | 0.29237170472273677<\/td>\n<\/tr>\n | \n| 74<\/td>\n | 0.27563735581699916<\/td>\n<\/tr>\n | \n| 75<\/td>\n | 0.25881904510252074<\/td>\n<\/tr>\n | \n| 76<\/td>\n | 0.24192189559966767<\/td>\n<\/tr>\n | \n| 77<\/td>\n | 0.22495105434386514<\/td>\n<\/tr>\n | \n| 78<\/td>\n | 0.20791169081775923<\/td>\n<\/tr>\n | \n| 79<\/td>\n | 0.19080899537654491<\/td>\n<\/tr>\n | \n| 80<\/td>\n | 0.17364817766693041<\/td>\n<\/tr>\n | \n| 81<\/td>\n | 0.15643446504023092<\/td>\n<\/tr>\n | \n| 82<\/td>\n | 0.13917310096006546<\/td>\n<\/tr>\n | \n| 83<\/td>\n | 0.12186934340514749<\/td>\n<\/tr>\n | \n| 84<\/td>\n | 0.10452846326765346<\/td>\n<\/tr>\n | \n| 85<\/td>\n | 0.08715574274765836<\/td>\n<\/tr>\n | \n| 86<\/td>\n | 0.06975647374412523<\/td>\n<\/tr>\n | \n| 87<\/td>\n | 0.052335956242943966<\/td>\n<\/tr>\n | \n| 88<\/td>\n | 0.03489949670250108<\/td>\n<\/tr>\n | \n| 89<\/td>\n | 0.0174524064372836<\/td>\n<\/tr>\n | \n| 90<\/td>\n | 0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n Nale\u017cy pami\u0119ta\u0107, \u017ce cos(\u03b8) = sin(90\u00b0 \u2013 \u03b8), co jest przydatne do szybkiego odwo\u0142ywania si\u0119 do wykres\u00f3w projektowych.<\/p>\n Tabela funkcji tangensowych<\/h2>\nTangens to stosunek d\u0142ugo\u015bci bok\u00f3w przeciwleg\u0142ych do s\u0105siednich, rosn\u0105cy od 0 do niesko\u0144czono\u015bci, gdy k\u0105t zbli\u017ca si\u0119 do 90\u00b0. Jest on kluczowy przy obliczaniu nachylenia ramp lub skoku gwintu w elementach z\u0142\u0105cznych.<\/p>\n \n \n\n\n| K\u0105t (\u00b0)<\/th>\n | warto\u015b\u0107 opalenizny<\/th>\n<\/tr>\n<\/thead>\n | \n\n| 1<\/td>\n | 0.017455064928217585<\/td>\n<\/tr>\n | \n| 2<\/td>\n | 0.03492076949174773<\/td>\n<\/tr>\n | \n| 3<\/td>\n | 0.052407779283041196<\/td>\n<\/tr>\n | \n| 4<\/td>\n | 0.06992681194351041<\/td>\n<\/tr>\n | \n| 5<\/td>\n | 0.08748866352592401<\/td>\n<\/tr>\n | \n| 6<\/td>\n | 0.10510423526567646<\/td>\n<\/tr>\n | \n| 7<\/td>\n | 0.1227845609029046<\/td>\n<\/tr>\n | \n| 8<\/td>\n | 0.14054083470239145<\/td>\n<\/tr>\n | \n| 9<\/td>\n | 0.15838444032453627<\/td>\n<\/tr>\n | \n| 10<\/td>\n | 0.17632698070846497<\/td>\n<\/tr>\n | \n| 11<\/td>\n | 0.19438030913771848<\/td>\n<\/tr>\n | \n| 12<\/td>\n | 0.2125565616700221<\/td>\n<\/tr>\n | \n| 13<\/td>\n | 0.2308681911255631<\/td>\n<\/tr>\n | \n| 14<\/td>\n | 0.24932800284318068<\/td>\n<\/tr>\n | \n| 15<\/td>\n | 0.2679491924311227<\/td>\n<\/tr>\n | \n| 16<\/td>\n | 0.2867453857588079<\/td>\n<\/tr>\n | \n| 17<\/td>\n | 0.30573068145866033<\/td>\n<\/tr>\n | \n| 18<\/td>\n | 0.3249196962329063<\/td>\n<\/tr>\n | \n| 19<\/td>\n | 0.34432761328966527<\/td>\n<\/tr>\n | \n| 20<\/td>\n | 0.36397023426620234<\/td>\n<\/tr>\n | \n| 21<\/td>\n | 0.3838640350354158<\/td>\n<\/tr>\n | \n| 22<\/td>\n | 0.4040262258351568<\/td>\n<\/tr>\n | \n| 23<\/td>\n | 0.4244748162096047<\/td>\n<\/tr>\n | \n| 24<\/td>\n | 0.4452286853085361<\/td>\n<\/tr>\n | \n| 25<\/td>\n | 0.4663076581549986<\/td>\n<\/tr>\n | \n| 26<\/td>\n | 0.4877325885658614<\/td>\n<\/tr>\n | \n| 27<\/td>\n | 0.5095254494944288<\/td>\n<\/tr>\n | \n| 28<\/td>\n | 0.5317094316614788<\/td>\n<\/tr>\n | \n| 29<\/td>\n | 0.554309051452769<\/td>\n<\/tr>\n | \n| 30<\/td>\n | 0.5773502691896257<\/td>\n<\/tr>\n | \n| 31<\/td>\n | 0.6008606190275604<\/td>\n<\/tr>\n | \n| 32<\/td>\n | 0.6248693519093275<\/td>\n<\/tr>\n | \n| 33<\/td>\n | 0.6494075931975104<\/td>\n<\/tr>\n | \n| 34<\/td>\n | 0.6745085168424265<\/td>\n<\/tr>\n | \n| 35<\/td>\n | 0.7002075382097097<\/td>\n<\/tr>\n | \n| 36<\/td>\n | 0.7265425280053609<\/td>\n<\/tr>\n | \n| 37<\/td>\n | 0.7535540501027942<\/td>\n<\/tr>\n | \n| 38<\/td>\n | 0.7812856265067174<\/td>\n<\/tr>\n | \n| 39<\/td>\n | 0.8097840331950072<\/td>\n<\/tr>\n | \n| 40<\/td>\n | 0.8390996311772799<\/td>\n<\/tr>\n | \n| 41<\/td>\n | 0.8692867378162267<\/td>\n<\/tr>\n | \n| 42<\/td>\n | 0.9004040442978399<\/td>\n<\/tr>\n | \n| 43<\/td>\n | 0.9325150861376618<\/td>\n<\/tr>\n | \n| 44<\/td>\n | 0.9656887748070739<\/td>\n<\/tr>\n | \n| 45<\/td>\n | 0.9999999999999999<\/td>\n<\/tr>\n | \n| 46<\/td>\n | 1.0355303137905693<\/td>\n<\/tr>\n | \n| 47<\/td>\n | 1.0723687100246826<\/td>\n<\/tr>\n | \n| 48<\/td>\n | 1.1106125148291927<\/td>\n<\/tr>\n | \n| 49<\/td>\n | 1.1503684072210092<\/td>\n<\/tr>\n | \n| 50<\/td>\n | 1.19175359259421<\/td>\n<\/tr>\n | \n| 51<\/td>\n | 1.234897156535051<\/td>\n<\/tr>\n | \n| 52<\/td>\n | 1.2799416321930785<\/td>\n<\/tr>\n | \n| 53<\/td>\n | 1.3270448216204098<\/td>\n<\/tr>\n | \n| 54<\/td>\n | 1.3763819204711733<\/td>\n<\/tr>\n | \n| 55<\/td>\n | 1.4281480067421144<\/td>\n<\/tr>\n | \n| 56<\/td>\n | 1.4825609685127403<\/td>\n<\/tr>\n | \n| 57<\/td>\n | 1.5398649638145827<\/td>\n<\/tr>\n | \n| 58<\/td>\n | 1.6003345290410506<\/td>\n<\/tr>\n | \n| 59<\/td>\n | 1.6642794823505173<\/td>\n<\/tr>\n | \n| 60<\/td>\n | 1.7320508075688767<\/td>\n<\/tr>\n | \n| 61<\/td>\n | 1.8040477552714235<\/td>\n<\/tr>\n | \n| 62<\/td>\n | 1.8807264653463318<\/td>\n<\/tr>\n | \n| 63<\/td>\n | 1.9626105055051503<\/td>\n<\/tr>\n | \n| 64<\/td>\n | 2.050303841579296<\/td>\n<\/tr>\n | \n| 65<\/td>\n | 2.1445069205095586<\/td>\n<\/tr>\n | \n| 66<\/td>\n | 2.246036773904215<\/td>\n<\/tr>\n | \n| 67<\/td>\n | 2.355852365823753<\/td>\n<\/tr>\n | \n| 68<\/td>\n | 2.4750868534162946<\/td>\n<\/tr>\n | \n| 69<\/td>\n | 2.6050890646938023<\/td>\n<\/tr>\n | \n| 70<\/td>\n | 2.7474774194546216<\/td>\n<\/tr>\n | \n| 71<\/td>\n | 2.904210877675822<\/td>\n<\/tr>\n | \n| 72<\/td>\n | 3.0776835371752526<\/td>\n<\/tr>\n | \n| 73<\/td>\n | 3.2708526184841404<\/td>\n<\/tr>\n | \n| 74<\/td>\n | 3.4874144438409087<\/td>\n<\/tr>\n | \n| 75<\/td>\n | 3.7320508075688776<\/td>\n<\/tr>\n | \n| 76<\/td>\n | 4.0107809335358455<\/td>\n<\/tr>\n | \n| 77<\/td>\n | 4.331475874284153<\/td>\n<\/tr>\n | \n| 78<\/td>\n | 4.704630109478456<\/td>\n<\/tr>\n | \n| 79<\/td>\n | 5.144554015970307<\/td>\n<\/tr>\n | \n| 80<\/td>\n | 5.671281819617707<\/td>\n<\/tr>\n | \n| 81<\/td>\n | 6.313751514675041<\/td>\n<\/tr>\n | \n| 82<\/td>\n | 7.115369722384207<\/td>\n<\/tr>\n | \n| 83<\/td>\n | 8.144346427974593<\/td>\n<\/tr>\n | \n| 84<\/td>\n | 9.514364454222587<\/td>\n<\/tr>\n | \n| 85<\/td>\n | 11.43005230276132<\/td>\n<\/tr>\n | \n| 86<\/td>\n | 14.300666256711942<\/td>\n<\/tr>\n | \n| 87<\/td>\n | 19.08113668772816<\/td>\n<\/tr>\n | \n| 88<\/td>\n | 28.636253282915515<\/td>\n<\/tr>\n | \n| 89<\/td>\n | 57.289961630759144<\/td>\n<\/tr>\n | \n| 90<\/td>\n | Niezdefiniowany (zbli\u017ca si\u0119 do niesko\u0144czono\u015bci)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n Tan(45\u00b0) = 1, kluczowy parametr dla tr\u00f3jk\u0105t\u00f3w r\u00f3wnobocznych w symetrii strukturalnej.<\/p>\n Tabela funkcji cotangens<\/h2>\nCotangens to odwrotno\u015b\u0107 stycznej, malej\u0105ca od niesko\u0144czono\u015bci przy 0\u00b0 do 0 przy 90\u00b0. Jest to przydatne przy obliczaniu nachylenia odwrotnego w rysunkach technicznych lub analizie kinematycznej.<\/p>\n \n \n\n\n| K\u0105t (\u00b0)<\/th>\n | warto\u015b\u0107 \u0142\u00f3\u017ceczka<\/th>\n<\/tr>\n<\/thead>\n | \n\n| 1<\/td>\n | 57.289961630759144<\/td>\n<\/tr>\n | \n| 2<\/td>\n | 28.636253282915515<\/td>\n<\/tr>\n | \n| 3<\/td>\n | 19.08113668772816<\/td>\n<\/tr>\n | \n| 4<\/td>\n | 14.300666256711942<\/td>\n<\/tr>\n | \n| 5<\/td>\n | 11.43005230276132<\/td>\n<\/tr>\n | \n| 6<\/td>\n | 9.514364454222587<\/td>\n<\/tr>\n | \n| 7<\/td>\n | 8.144346427974593<\/td>\n<\/tr>\n | \n| 8<\/td>\n | 7.115369722384207<\/td>\n<\/tr>\n | \n| 9<\/td>\n | 6.313751514675041<\/td>\n<\/tr>\n | \n| 10<\/td>\n | 5.671281819617707<\/td>\n<\/tr>\n | \n| 11<\/td>\n | 5.144554015970307<\/td>\n<\/tr>\n | \n| 12<\/td>\n | 4.704630109478456<\/td>\n<\/tr>\n | \n| 13<\/td>\n | 4.331475874284153<\/td>\n<\/tr>\n | \n| 14<\/td>\n | 4.0107809335358455<\/td>\n<\/tr>\n | \n| 15<\/td>\n | 3.7320508075688776<\/td>\n<\/tr>\n | \n| 16<\/td>\n | 3.4874144438409087<\/td>\n<\/tr>\n | \n| 17<\/td>\n | 3.2708526184841404<\/td>\n<\/tr>\n | \n| 18<\/td>\n | 3.0776835371752526<\/td>\n<\/tr>\n | \n| 19<\/td>\n | 2.904210877675822<\/td>\n<\/tr>\n | \n| 20<\/td>\n | 2.7474774194546216<\/td>\n<\/tr>\n | \n| 21<\/td>\n | 2.6050890646938023<\/td>\n<\/tr>\n | \n| 22<\/td>\n | 2.4750868534162946<\/td>\n<\/tr>\n | \n| 23<\/td>\n | 2.355852365823753<\/td>\n<\/tr>\n | \n| 24<\/td>\n | 2.246036773904215<\/td>\n<\/tr>\n | \n| 25<\/td>\n | 2.1445069205095586<\/td>\n<\/tr>\n | \n| 26<\/td>\n | 2.050303841579296<\/td>\n<\/tr>\n | \n| 27<\/td>\n | 1.9626105055051503<\/td>\n<\/tr>\n | \n| 28<\/td>\n | 1.8807264653463318<\/td>\n<\/tr>\n | \n| 29<\/td>\n | 1.8040477552714235<\/td>\n<\/tr>\n | \n| 30<\/td>\n | 1.7320508075688767<\/td>\n<\/tr>\n | \n| 31<\/td>\n | 1.6642794823505173<\/td>\n<\/tr>\n | \n| 32<\/td>\n | 1.6003345290410506<\/td>\n<\/tr>\n | \n| 33<\/td>\n | 1.5398649638145827<\/td>\n<\/tr>\n | \n| 34<\/td>\n | 1.4825609685127403<\/td>\n<\/tr>\n | \n| 35<\/td>\n | 1.4281480067421144<\/td>\n<\/tr>\n | \n| 36<\/td>\n | 1.3763819204711733<\/td>\n<\/tr>\n | \n| 37<\/td>\n | 1.3270448216204098<\/td>\n<\/tr>\n | \n| 38<\/td>\n | 1.2799416321930785<\/td>\n<\/tr>\n | \n| 39<\/td>\n | 1.234897156535051<\/td>\n<\/tr>\n | \n| 40<\/td>\n | 1.19175359259421<\/td>\n<\/tr>\n | \n| 41<\/td>\n | 1.1503684072210092<\/td>\n<\/tr>\n | \n| 42<\/td>\n | 1.1106125148291927<\/td>\n<\/tr>\n | \n| 43<\/td>\n | 1.0723687100246826<\/td>\n<\/tr>\n | \n| 44<\/td>\n | 1.0355303137905693<\/td>\n<\/tr>\n | \n| 45<\/td>\n | 1.000000000000000<\/td>\n<\/tr>\n | \n| 46<\/td>\n | 0.9656887748070739<\/td>\n<\/tr>\n | \n| 47<\/td>\n | 0.9325150861376618<\/td>\n<\/tr>\n | \n| 48<\/td>\n | 0.9004040442978399<\/td>\n<\/tr>\n | \n| 49<\/td>\n | 0.8692867378162267<\/td>\n<\/tr>\n | \n| 50<\/td>\n | 0.8390996311772799<\/td>\n<\/tr>\n | \n| 51<\/td>\n | 0.8097840331950072<\/td>\n<\/tr>\n | \n| 52<\/td>\n | 0.7812856265067174<\/td>\n<\/tr>\n | \n| 53<\/td>\n | 0.7535540501027942<\/td>\n<\/tr>\n | \n| 54<\/td>\n | 0.7265425280053609<\/td>\n<\/tr>\n | \n| 55<\/td>\n | 0.7002075382097097<\/td>\n<\/tr>\n | \n| 56<\/td>\n | 0.6745085168424265<\/td>\n<\/tr>\n | \n| 57<\/td>\n | 0.6494075931975104<\/td>\n<\/tr>\n | \n| 58<\/td>\n | 0.6248693519093275<\/td>\n<\/tr>\n | \n| 59<\/td>\n | 0.6008606190275604<\/td>\n<\/tr>\n | \n| 60<\/td>\n | 0.5773502691896257<\/td>\n<\/tr>\n | \n| 61<\/td>\n | 0.554309051452769<\/td>\n<\/tr>\n | \n| 62<\/td>\n | 0.5317094316614788<\/td>\n<\/tr>\n | \n| 63<\/td>\n | 0.5095254494944288<\/td>\n<\/tr>\n | \n| 64<\/td>\n | 0.4877325885658614<\/td>\n<\/tr>\n | \n| 65<\/td>\n | 0.4663076581549986<\/td>\n<\/tr>\n | \n| 66<\/td>\n | 0.4452286853085361<\/td>\n<\/tr>\n | \n| 67<\/td>\n | 0.4244748162096047<\/td>\n<\/tr>\n | \n| 68<\/td>\n | 0.4040262258351568<\/td>\n<\/tr>\n | \n| 69<\/td>\n | 0.3838640350354158<\/td>\n<\/tr>\n | \n| 70<\/td>\n | 0.36397023426620234<\/td>\n<\/tr>\n | \n| 71<\/td>\n | 0.34432761328966527<\/td>\n<\/tr>\n | \n| 72<\/td>\n | 0.3249196962329063<\/td>\n<\/tr>\n | \n| 73<\/td>\n | 0.30573068145866033<\/td>\n<\/tr>\n | \n| 74<\/td>\n | 0.2867453857588079<\/td>\n<\/tr>\n | \n| 75<\/td>\n | 0.2679491924311227<\/td>\n<\/tr>\n | \n| 76<\/td>\n | 0.24932800284318068<\/td>\n<\/tr>\n | \n| 77<\/td>\n | 0.2308681911255631<\/td>\n<\/tr>\n | \n| 78<\/td>\n | 0.2125565616700221<\/td>\n<\/tr>\n | \n| 79<\/td>\n | 0.19438030913771848<\/td>\n<\/tr>\n | \n| 80<\/td>\n | 0.17632698070846497<\/td>\n<\/tr>\n | \n| 81<\/td>\n | 0.15838444032453627<\/td>\n<\/tr>\n | \n| 82<\/td>\n | 0.14054083470239145<\/td>\n<\/tr>\n | \n| 83<\/td>\n | 0.1227845609029046<\/td>\n<\/tr>\n | \n| 84<\/td>\n | 0.10510423526567646<\/td>\n<\/tr>\n | \n| 85<\/td>\n | 0.08748866352592401<\/td>\n<\/tr>\n | \n| 86<\/td>\n | 0.06992681194351041<\/td>\n<\/tr>\n | \n| 87<\/td>\n | 0.052407779283041196<\/td>\n<\/tr>\n | \n| 88<\/td>\n | 0.03492076949174773<\/td>\n<\/tr>\n | \n| 89<\/td>\n | 0.017455064928217585<\/td>\n<\/tr>\n | \n| 90<\/td>\n | 0 (zbli\u017ca si\u0119 do 0)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n Cot(\u03b8) = tan(90\u00b0 \u2013 \u03b8), co zapewnia wygodn\u0105 zale\u017cno\u015b\u0107 do weryfikacji.<\/p>\n Zastosowania w projektowaniu mechanicznym<\/h2>\nW in\u017cynierii mechanicznej funkcje te s\u0105 stosowane do obliczania k\u0105t\u00f3w gwintu \u015brub (np. 60\u00b0 w gwintach metrycznych), obliczania si\u0142 w kratownicach lub projektowania nachylonych element\u00f3w z\u0142\u0105cznych. Na przyk\u0142ad, tan(\u03b8) okre\u015bla stosunek wysoko\u015bci do d\u0142ugo\u015bci w systemach przeno\u015bnik\u00f3w ta\u015bmowych, a sin i cos obliczaj\u0105 sk\u0142adowe grawitacyjne w analizie obci\u0105\u017ce\u0144.<\/p>\n \n- Oblicz napr\u0119\u017cenie \u015bcinaj\u0105ce w po\u0142\u0105czeniach k\u0105towych za pomoc\u0105 sin(\u03b8).<\/li>\n
- W mechanizmach klinowych do okre\u015blenia si\u0142y normalnej nale\u017cy stosowa\u0107 cos(\u03b8).<\/li>\n
- Zastosuj tan(\u03b8) do k\u0105t\u00f3w tarcia w urz\u0105dzeniach zaciskowych.<\/li>\n
- Zastosuj cot(\u03b8) w profilach z\u0119b\u00f3w przek\u0142adni dla prze\u0142o\u017ce\u0144 odwrotnych.<\/li>\n<\/ol>\n
Zintegruj si\u0119 z oprogramowaniem takim jak AutoCAD, aby uzyska\u0107 precyzyjne modelowanie i mie\u0107 pewno\u015b\u0107, \u017ce projekty spe\u0142niaj\u0105 normy bezpiecze\u0144stwa.<\/p>\n Cz\u0119sto zadawane pytania (FAQ)<\/h2>\n\n Jak dok\u0142adne s\u0105 te warto\u015bci trygonometryczne?<\/h3>\nWarto\u015bci s\u0105 obliczane do 15 miejsc po przecinku przy u\u017cyciu standardowych bibliotek matematycznych, co jest wystarczaj\u0105ce dla precyzji in\u017cynierskiej; w razie potrzeby zaokr\u0105glane w celu unikni\u0119cia b\u0142\u0119d\u00f3w.<\/p>\n Dlaczego nale\u017cy u\u017cywa\u0107 stopni zamiast radian\u00f3w?<\/h3>\nStopnie powszechnie wyst\u0119puj\u0105 w rysunkach technicznych; w przypadku narz\u0119dzi obliczeniowych, takich jak MATLAB lub Python, mo\u017cna je przeliczy\u0107 na radiany (\u03b8_rad = \u03b8_deg * \u03c0 \/ 180).<\/p>\n Co zrobi\u0107, je\u015bli potrzebuj\u0119 warto\u015bci k\u0105t\u00f3w wi\u0119kszych ni\u017c 90\u00b0?<\/h3>\nZastosuj w\u0142a\u015bciwo\u015bci okresowe: sin(180\u00b0 \u2013 \u03b8) = sin(\u03b8), cos(180\u00b0 \u2013 \u03b8) = -cos(\u03b8); odpowiednio rozszerz tabele, aby umo\u017cliwi\u0107 analiz\u0119 pe\u0142nego okr\u0119gu w obrotach.<\/p>\n Jak te funkcje maj\u0105 zastosowanie w projektowaniu element\u00f3w z\u0142\u0105cznych?<\/h3>\nW geometrii gwint\u00f3w tan(30\u00b0) \u2248 0,577 pomaga obliczy\u0107 k\u0105ty natarcia; sin i cos pozwalaj\u0105 obliczy\u0107 si\u0142y osiowe i promieniowe dla specyfikacji momentu obrotowego.<\/p>\n Czy mog\u0119 interpolowa\u0107 warto\u015bci pomi\u0119dzy tabelami?<\/h3>\nTak, do przybli\u017ce\u0144 nale\u017cy stosowa\u0107 interpolacj\u0119 liniow\u0105, jednak w celu uzyskania wi\u0119kszej dok\u0142adno\u015bci nale\u017cy pos\u0142ugiwa\u0107 si\u0119 kalkulatorami lub oprogramowaniem do obliczania dok\u0142adnych warto\u015bci k\u0105t\u00f3w nieca\u0142kowitych.<\/p>\n Jaki jest zwi\u0105zek mi\u0119dzy kolorem opalenizny a kolorem cot?<\/h3>\nCot(\u03b8) = 1 \/ tan(\u03b8), przydatne do upraszczania r\u00f3wna\u0144 w analizie stabilno\u015bci konstrukcji mechanicznych.<\/p>\n<\/div>\n <\/p>","protected":false},"excerpt":{"rendered":" Zarys artyku\u0142u W tym artykule przedstawiono szczeg\u00f3\u0142ow\u0105 tabel\u0119 funkcji trygonometrycznych, zoptymalizowan\u0105 do praktycznego zastosowania w in\u017cynierii mechanicznej. Jej struktura jest nast\u0119puj\u0105ca: Wprowadzenie do funkcji trygonometrycznych, Definicje i podstawowe zasady, Tabela funkcji sinus, Tabela funkcji cosinus, Tabela funkcji tangens, Tabela funkcji cotangens, Zastosowania w projektowaniu mechanicznym, Cz\u0119sto zadawane pytania (FAQ), Wprowadzenie do funkcji trygonometrycznych, Funkcje trygonometryczne [\u2026]<\/p>","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[220],"tags":[],"class_list":["post-5735","post","type-post","status-publish","format-standard","hentry","category-technical-documentation-and-references"],"_links":{"self":[{"href":"https:\/\/korea-transmission.com\/pl\/wp-json\/wp\/v2\/posts\/5735","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/korea-transmission.com\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/korea-transmission.com\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/korea-transmission.com\/pl\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/korea-transmission.com\/pl\/wp-json\/wp\/v2\/comments?post=5735"}],"version-history":[{"count":2,"href":"https:\/\/korea-transmission.com\/pl\/wp-json\/wp\/v2\/posts\/5735\/revisions"}],"predecessor-version":[{"id":5737,"href":"https:\/\/korea-transmission.com\/pl\/wp-json\/wp\/v2\/posts\/5735\/revisions\/5737"}],"wp:attachment":[{"href":"https:\/\/korea-transmission.com\/pl\/wp-json\/wp\/v2\/media?parent=5735"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/korea-transmission.com\/pl\/wp-json\/wp\/v2\/categories?post=5735"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/korea-transmission.com\/pl\/wp-json\/wp\/v2\/tags?post=5735"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}} | | | |