tan(1.9*c)*tan(1.9)+cot(- ... n(pi)^(2)/2-cos(pi)^(2)/2 (уравнение)

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    Найду корень уравнения: tan(1.9*c)*tan(1.9)+cot(-5*pi/6)^(2)=-sin(pi)^(2)/2-cos(pi)^(2)/2

    Решение

    Вы ввели [src]
                                          2           2    
       /19*c\    /19\      2/-5*pi\   -sin (pi)    cos (pi)
    tan|----|*tan|--| + cot |-----| = ---------- - --------
       \ 10 /    \10/       \  6  /       2           2    
    tan(1910)tan(19c10)+cot2(5π6)=cos2(π)2+(1)sin2(π)2\tan{\left(\frac{19}{10} \right)} \tan{\left(\frac{19 c}{10} \right)} + \cot^{2}{\left(- \frac{5 \pi}{6} \right)} = - \frac{\cos^{2}{\left(\pi \right)}}{2} + \frac{\left(-1\right) \sin^{2}{\left(\pi \right)}}{2}
    Подробное решение
    Дано уравнение
    tan(1910)tan(19c10)+cot2(5π6)=cos2(π)2+(1)sin2(π)2\tan{\left(\frac{19}{10} \right)} \tan{\left(\frac{19 c}{10} \right)} + \cot^{2}{\left(- \frac{5 \pi}{6} \right)} = - \frac{\cos^{2}{\left(\pi \right)}}{2} + \frac{\left(-1\right) \sin^{2}{\left(\pi \right)}}{2}
    - это простейшее тригонометрическое ур-ние
    Разделим обе части ур-ния на tan(19/10)

    Ур-ние превратится в
    tan(19c10)=72tan(1910)\tan{\left(\frac{19 c}{10} \right)} = - \frac{7}{2 \tan{\left(\frac{19}{10} \right)}}
    Это ур-ние преобразуется в
    19c10=πn+atan(72tan(1910))\frac{19 c}{10} = \pi n + \operatorname{atan}{\left(- \frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}
    Или
    19c10=πnatan(72tan(1910))\frac{19 c}{10} = \pi n - \operatorname{atan}{\left(\frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}
    , где n - любое целое число
    Разделим обе части полученного ур-ния на
    1910\frac{19}{10}
    получим ответ:
    c1=10πn1910atan(72tan(1910))19c_{1} = \frac{10 \pi n}{19} - \frac{10 \operatorname{atan}{\left(\frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}}{19}
    График
    0-80-60-40-2020406080-100100-5000050000
    Быстрый ответ [src]
                 /    7    \
         -10*atan|---------|
                 |     /19\|
                 |2*tan|--||
                 \     \10//
    c1 = -------------------
                  19        
    c1=10atan(72tan(1910))19c_{1} = - \frac{10 \operatorname{atan}{\left(\frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}}{19}
    Сумма и произведение корней [src]
    сумма
               /    7    \
        10*atan|---------|
               |     /19\|
               |2*tan|--||
               \     \10//
    0 - ------------------
                19        
    010atan(72tan(1910))190 - \frac{10 \operatorname{atan}{\left(\frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}}{19}
    =
            /    7    \
    -10*atan|---------|
            |     /19\|
            |2*tan|--||
            \     \10//
    -------------------
             19        
    10atan(72tan(1910))19- \frac{10 \operatorname{atan}{\left(\frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}}{19}
    произведение
              /    7    \
      -10*atan|---------|
              |     /19\|
              |2*tan|--||
              \     \10//
    1*-------------------
               19        
    1(10atan(72tan(1910))19)1 \left(- \frac{10 \operatorname{atan}{\left(\frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}}{19}\right)
    =
            /    7    \
    -10*atan|---------|
            |     /19\|
            |2*tan|--||
            \     \10//
    -------------------
             19        
    10atan(72tan(1910))19- \frac{10 \operatorname{atan}{\left(\frac{7}{2 \tan{\left(\frac{19}{10} \right)}} \right)}}{19}
    Численный ответ [src]
    c1 = 69.9058911819971
    c2 = 91.400998811822
    c3 = -97.0945604035656
    c4 = 2.11362865716471
    c5 = -7.80719024890832
    c6 = 26.9156759223473
    c7 = -83.8668018621349
    c8 = -67.3321036853465
    c9 = -44.1835262378428
    c10 = 40.143434463778
    c11 = 56.6781326405664
    c12 = -6.15372043122948
    c13 = 36.8364948284203
    c14 = 58.3316024582452
    c15 = 64.9454817289606
    c16 = -78.9063924090984
    c17 = -2.84678079587181
    c18 = 74.8663006350336
    c19 = -98.7480302212444
    c20 = -64.0251640499888
    c21 = -29.3022978787332
    c22 = 86.4405893587855
    c23 = 79.8267100880701
    c24 = 41.7969042814568
    c25 = -47.4904658732004
    c26 = 38.4899646460992
    c27 = -54.1043451439158
    c28 = -37.5696469671274
    c29 = -60.7182244146312
    c30 = 98.0148780825373
    c31 = -82.2133320444561
    c32 = 101.321817717895
    c33 = 7.07403811020122
    c34 = 31.8760853753838
    c35 = 96.3614082648585
    c36 = -70.6390433207042
    c37 = -55.7578149615946
    c38 = -1.19331097819297
    c39 = -9.46066006658716
    c40 = 94.7079384471797
    c41 = -85.5202716798137
    c42 = -19.3814789726602
    c43 = 63.2920119112817
    c44 = -59.0647545969523
    c45 = -25.9953582433755
    c46 = -95.4410905858868
    c47 = -16.0745393373025
    c48 = 50.064253369851
    c49 = 15.3413871985954
    c50 = -68.9855735030253
    c51 = 83.1336497234278
    c52 = 48.4107835521722
    c53 = -50.7974055085581
    c54 = 59.9850722759241
    c55 = 55.0246628228875
    c56 = 66.5989515466394
    c57 = -30.9557676964121
    c58 = -35.9161771494486
    c59 = 10.3809777455589
    c60 = 8.72750792788006
    c61 = 73.2128308173548
    c62 = -32.6092375140909
    c63 = -11.114129884266
    c64 = 76.5197704527124
    c65 = 21.9552664693108
    c66 = -57.4112847792735
    c67 = 53.3711930052087
    c68 = -75.5994527737407
    c69 = 20.3017966516319
    c70 = -21.034948790339
    c71 = 18.6483268339531
    c72 = 0.460158839485869
    c73 = -49.1439356908793
    c74 = -93.7876207682079
    c75 = 25.2622061046684
    c76 = -40.8765866024851
    c77 = 93.0544686295008
    c78 = 45.1038439168145
    c79 = -65.6786338676677
    c80 = 12.0344475632377
    c81 = 28.5691457400261
    c82 = 30.222615557705
    c83 = -77.2529225914195
    c84 = 88.0940591764643
    c85 = 5.42056829252238
    c86 = 35.1830250107415
    c87 = -45.8369960555216
    c88 = 16.9948570162743
    c89 = -87.1737414974926
    c90 = 46.7573137344934
    c91 = -17.7280091549814
    c92 = 68.2524213643183
    c93 = -12.7675997019448
    c94 = -39.2231167848063
    c95 = 84.7871195411066
    c96 = -73.9459829560619
    c97 = -92.1341509505291
    c98 = -27.6488280610544
    c99 = 78.1732402703913
    c100 = -22.6884186080179
    c101 = -88.8272113151714
    График
    tan(1.9*c)*tan(1.9)+cot(- ... n(pi)^(2)/2-cos(pi)^(2)/2 (уравнение) /media/krcore-image-pods/hash/equation/b/a5/d6753d5bcda840ce93a3f88d53bc4.png