sin(x)=0,42 (уравнение)

Найду корень уравнения: sin(x)=0,42

Вы ввели

         21
sin(x) = --
         50

$$\sin{\left(x \right)} = \frac{21}{50}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{21}{50}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{21}{50} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{21}{50} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{21}{50} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{21}{50} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

              /21\
x1 = pi - asin|--|
              \50/

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{21}{50} \right)}$$

         /21\
x2 = asin|--|
         \50/

$$x_{2} = \operatorname{asin}{\left(\frac{21}{50} \right)}$$

Сумма и произведение корней

сумма

             /21\       /21\
0 + pi - asin|--| + asin|--|
             \50/       \50/

$$\operatorname{asin}{\left(\frac{21}{50} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{21}{50} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

  /         /21\\     /21\
1*|pi - asin|--||*asin|--|
  \         \50//     \50/

$$1 \left(\pi - \operatorname{asin}{\left(\frac{21}{50} \right)}\right) \operatorname{asin}{\left(\frac{21}{50} \right)}$$

=

/         /21\\     /21\
|pi - asin|--||*asin|--|
\         \50//     \50/

$$\left(\pi - \operatorname{asin}{\left(\frac{21}{50} \right)}\right) \operatorname{asin}{\left(\frac{21}{50} \right)}$$

Численный ответ

x1 = -41.2741498167372

x2 = -37.2656665230076

x3 = 31.8493718559678

x4 = -5.8497399871097

x5 = 46.690444483777

x6 = 34.1240738694178

x7 = 75.8316690062249

x8 = 82.1148543134045

x9 = 8.99133264069949

x10 = -22.4245938951984

x11 = -78.9732616598147

x12 = -62.398407751726

x13 = 71.8231857124954

x14 = -66.4068910454555

x15 = -12.1329252942893

x16 = 44.415742470327

x17 = 69.5484836990453

x18 = -68.6815930589056

x19 = -97.8228175813535

x20 = -162.929372666599

x21 = 15.2745179478791

x22 = 19.2830012416086

x23 = 96.9559269412137

x24 = -47.5573351239168

x25 = -30.982481215828

x26 = 65.5400004053158

x27 = -810.097459306097

x28 = -53.8405204310964

x29 = 163.796263306739

x30 = -100.097519594804

x31 = 27.8408885622383

x32 = 78.1063710196749

x33 = 63.2652983918657

x34 = -91.5396322741739

x35 = 59.2568150981362

x36 = -3.57503797365968

x37 = 50.6989277775066

x38 = 52.9736297909566

x39 = 56.9821130846862

x40 = -9.85822328083927

x41 = 21.5577032550587

x42 = -60.123705738276

x43 = 0.433445320069886

x44 = 94.6812249277637

x45 = -18.4161106014689

x46 = 12.9998159344291

x47 = 88.3980396205841

x48 = -72.6900763526351

x49 = -81.2479636732647

x50 = -43.5488518301872

x51 = -28.707779202378

x52 = -74.9647783660852

x53 = -34.9909645095576

x54 = -16.1414085880189

x55 = 38.1325571631474

x56 = 84.3895563268545

x57 = 90.6727416340341

x58 = 2.70814733351991

x59 = -49.8320371373668

x60 = -39665.3153989047

x61 = -24.6992959086485

x62 = -56.1152224445464

x63 = -85.2564469669943

x64 = 40.4072591765974

x65 = 6.71663062724947

x66 = -93.8143342876239

x67 = 1960.7872611601

x68 = 25.5661865487882

x69 = 100.964410234943

x70 = -87.5311489804443

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