sin(x)=√3/4 (уравнение)

Найду корень уравнения: sin(x)=√3/4

Вы ввели

           ___
         \/ 3 
sin(x) = -----
           4  

$$\sin{\left(x \right)} = \frac{\sqrt{3}}{4}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{\sqrt{3}}{4}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{4} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{4} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

              /  ___\
              |\/ 3 |
x1 = pi - asin|-----|
              \  4  /

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{\sqrt{3}}{4} \right)}$$

         /  ___\
         |\/ 3 |
x2 = asin|-----|
         \  4  /

$$x_{2} = \operatorname{asin}{\left(\frac{\sqrt{3}}{4} \right)}$$

Сумма и произведение корней

сумма

             /  ___\       /  ___\
             |\/ 3 |       |\/ 3 |
0 + pi - asin|-----| + asin|-----|
             \  4  /       \  4  /

$$\operatorname{asin}{\left(\frac{\sqrt{3}}{4} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{\sqrt{3}}{4} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

  /         /  ___\\     /  ___\
  |         |\/ 3 ||     |\/ 3 |
1*|pi - asin|-----||*asin|-----|
  \         \  4  //     \  4  /

$$1 \left(\pi - \operatorname{asin}{\left(\frac{\sqrt{3}}{4} \right)}\right) \operatorname{asin}{\left(\frac{\sqrt{3}}{4} \right)}$$

=

/         /  ___\\     /  ___\
|         |\/ 3 ||     |\/ 3 |
|pi - asin|-----||*asin|-----|
\         \  4  //     \  4  /

$$\left(\pi - \operatorname{asin}{\left(\frac{\sqrt{3}}{4} \right)}\right) \operatorname{asin}{\left(\frac{\sqrt{3}}{4} \right)}$$

Численный ответ

x1 = -87.5167619035853

x2 = 25.5805736256473

x3 = 52.9592427140976

x4 = 65.5256133284567

x5 = 75.846056083084

x6 = -91.5540193510329

x7 = 6.73101770410852

x8 = -47.5717222007758

x9 = -78.9876487366738

x10 = 84.3751692499955

x11 = 78.0919839428159

x12 = -9.87261035769831

x13 = -18.4017235246098

x14 = -93.7999472107649

x15 = 31.8637589328269

x16 = -3.58942505051873

x17 = -5.83535291025065

x18 = 27.8265014853792

x19 = 69.5628707759044

x20 = 21.5433161781996

x21 = -81.2335765964057

x22 = -28.7221662792371

x23 = 34.1096867925588

x24 = 44.430129547186

x25 = 46.676057406918

x26 = -60.138092815135

x27 = 59.2424280212771

x28 = -74.9503912892261

x29 = 71.8087986356363

x30 = 68181.5375284624

x31 = -53.8549075079554

x32 = -24.6849088317894

x33 = -49.8176500605078

x34 = 15.26013087102

x35 = -66.4212781223146

x36 = -351.410544805128

x37 = -22.4389809720575

x38 = 50.7133148543656

x39 = -41.2885368935962

x40 = 0.447832396928933

x41 = -56.1008353676873

x42 = 13.0142030112881

x43 = 90.6583545571751

x44 = -68.6672059820465

x45 = -100.083132517944

x46 = -43.5344647533282

x47 = -62.3840206748669

x48 = -35.0053515864167

x49 = -72.7044634294942

x50 = 63.2796854687248

x51 = 40.3928720997384

x52 = -85.2708340438534

x53 = 96.9415398643547

x54 = -12.1185382174302

x55 = -16.1557956648779

x56 = -37.2512794461486

x57 = 2.69376025666086

x58 = 56.9965001615452

x59 = -97.8372046582125

x60 = 100.978797311802

x61 = 82.1292413902636

x62 = 19.2973883184677

x63 = 88.4124266974431

x64 = 94.6956120046227

x65 = 38.1469442400064

x66 = 8.97694556384045

x67 = -30.968094138969

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