sin(3*x-30)=0 (уравнение)

Найду корень уравнения: sin(3*x-30)=0

Вы ввели

sin(3*x - 30) = 0

$$\sin{\left(3 x - 30 \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(3 x - 30 \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\sin{\left(3 x - 30 \right)} = 0$$
Это ур-ние преобразуется в
$$3 x - 30 = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$3 x - 30 = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Или
$$3 x - 30 = 2 \pi n$$
$$3 x - 30 = 2 \pi n + \pi$$
, где n - любое целое число
Перенесём
$$-30$$
в правую часть ур-ния
с противоположным знаком, итого:
$$3 x = 2 \pi n + 30$$
$$3 x = 2 \pi n + \pi + 30$$
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = \frac{2 \pi n}{3} + 10$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{\pi}{3} + 10$$

Быстрый ответ

x1 = 10

$$x_{1} = 10$$

          pi
x2 = 10 + --
          3 

$$x_{2} = \frac{\pi}{3} + 10$$

Сумма и произведение корней

сумма

          pi
10 + 10 + --
          3 

$$10 + \left(\frac{\pi}{3} + 10\right)$$

=

     pi
20 + --
     3 

$$\frac{\pi}{3} + 20$$

произведение

   /     pi\
10*|10 + --|
   \     3 /

$$10 \left(\frac{\pi}{3} + 10\right)$$

=

      10*pi
100 + -----
        3  

$$\frac{10 \pi}{3} + 100$$

Численный ответ

x1 = 66.5486677646163

x2 = 27.8023583703422

x3 = 20.471975511966

x4 = -99.9557428756428

x5 = 56.0766922526503

x6 = -5.70796326794897

x7 = 97.9645943005142

x8 = -38.1710873550435

x9 = 53.9822971502571

x10 = -77.9645943005142

x11 = -51.7846555205993

x12 = 95.870199198121

x13 = 60.2654824574367

x14 = -29.7935069454707

x15 = 29.8967534727354

x16 = -80.0589894029074

x17 = 78.0678408277789

x18 = -40.2654824574367

x19 = -73.7758040957278

x20 = 18.3775804095728

x21 = 71.7846555205993

x22 = 100.058989402907

x23 = 93.7758040957278

x24 = 47.6991118430775

x25 = 40.3687289847013

x26 = -33.9822971502571

x27 = -53.8790506229925

x28 = 91.6814089933346

x29 = 90.634211442138

x30 = -25.6047167406843

x31 = 10.0

x32 = 75.9734457253857

x33 = 62.3598775598299

x34 = -21.4159265358979

x35 = 5.81120979521361

x36 = 3.71681469282041

x37 = 42.4631240870945

x38 = 756.651854003174

x39 = 80.162235930172

x40 = -91.57816246607

x41 = 16.2831853071796

x42 = -47.5958653158129

x43 = 64.4542726622231

x44 = -88.4365698124802

x45 = -89.4837673636768

x46 = -60.1622359301721

x47 = 579.675467850949

x48 = -44.4542726622231

x49 = -75.870199198121

x50 = 1.62241959042722

x51 = -95.7669526708564

x52 = -49.6902604182061

x53 = -14.0855436775217

x54 = -18.2743338823081

x55 = 88.5398163397448

x56 = -82.1533845053006

x57 = 44.5575191894877

x58 = -31.8879020478639

x59 = -23.5103216382911

x60 = -36.0766922526503

x61 = 119.955742875643

x62 = -62.2566310325652

x63 = -0.471975511965977

x64 = -1.51917306316258

x65 = 58.1710873550435

x66 = -58.0678408277789

x67 = -69.5870138909414

x68 = -84.2477796076938

x69 = 49.7935069454707

x70 = 31.9911485751286

x71 = 14.1887902047864

x72 = -27.6991118430775

x73 = 38.2743338823081

x74 = -97.8613477732496

x75 = 69.6902604182061

x76 = 51.8879020478639

x77 = 12.0943951023932

x78 = 7.9056048976068

x79 = -67.4926187885482

x80 = -3.61356816555577

x81 = -11.9911485751286

x82 = 82.2566310325652

x83 = -71.6814089933346

x84 = -45.5014702134197

x85 = 2520.13253021824

x86 = -7.80235837034216

x87 = 73.8790506229925

x88 = -19.3215314335047

x89 = 25.707963267949

x90 = 36.1799387799149

x91 = -16.1799387799149

x92 = 86.4454212373516

x93 = 84.3510261349584

x94 = -55.9734457253857

x95 = -93.6725575684632

x96 = -9.89675347273536

x97 = 34.0855436775217

График