sin(x+pi/6)=1/2 (уравнение)

Найду корень уравнения: sin(x+pi/6)=1/2

Вы ввели

   /    pi\      
sin|x + --| = 1/2
   \    6 /      

$$\sin{\left(x + \frac{\pi}{6} \right)} = \frac{1}{2}$$

Подробное решение

Дано уравнение
$$\sin{\left(x + \frac{\pi}{6} \right)} = \frac{1}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x + \frac{\pi}{6} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$x + \frac{\pi}{6} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
Или
$$x + \frac{\pi}{6} = 2 \pi n + \frac{\pi}{6}$$
$$x + \frac{\pi}{6} = 2 \pi n + \frac{5 \pi}{6}$$
, где n - любое целое число
Перенесём
$$\frac{\pi}{6}$$
в правую часть ур-ния
с противоположным знаком, итого:
$$x = 2 \pi n$$
$$x = 2 \pi n + \frac{2 \pi}{3}$$

Сумма и произведение корней

сумма

        2*pi
0 + 0 + ----
         3  

$$\left(0 + 0\right) + \frac{2 \pi}{3}$$

=

2*pi
----
 3  

$$\frac{2 \pi}{3}$$

произведение

    2*pi
1*0*----
     3  

$$1 \cdot 0 \cdot \frac{2 \pi}{3}$$

=

0

$$0$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     2*pi
x2 = ----
      3  

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

Численный ответ

x1 = -12.5663706143592

x2 = 27.2271363311115

x3 = 75.398223686155

x4 = 90.0589894029074

x5 = -50.2654824574367

x6 = -23.0383461263252

x7 = -62.8318530717959

x8 = 12.5663706143592

x9 = -35.6047167406843

x10 = 2.0943951023932

x11 = 77.4926187885482

x12 = 8.37758040957278

x13 = 96.342174710087

x14 = -161.268422884276

x15 = 87.9645943005142

x16 = 58.6430628670095

x17 = -67.0206432765823

x18 = -100.530964914873

x19 = -79.5870138909414

x20 = -87.9645943005142

x21 = 0.0

x22 = 33.5103216382911

x23 = 83.7758040957278

x24 = 37.6991118430775

x25 = -236.666646570431

x26 = -6.28318530717959

x27 = 43.9822971502571

x28 = -56.5486677646163

x29 = 94.2477796076938

x30 = -69.1150383789755

x31 = -31.4159265358979

x32 = 20.943951023932

x33 = 62.8318530717959

x34 = 18.8495559215388

x35 = -37.6991118430775

x36 = -48.1710873550435

x37 = 56.5486677646163

x38 = -75.398223686155

x39 = 81.6814089933346

x40 = -18.8495559215388

x41 = 31.4159265358979

x42 = -16.7551608191456

x43 = -41.8879020478639

x44 = -43.9822971502571

x45 = 71.2094334813686

x46 = -92.1533845053006

x47 = -54.4542726622231

x48 = -85.870199198121

x49 = -81.6814089933346

x50 = -4.18879020478639

x51 = -25.1327412287183

x52 = 50.2654824574367

x53 = 69.1150383789755

x54 = 108.908545324446

x55 = -98.4365698124802

x56 = 100.530964914873

x57 = -29.3215314335047

x58 = 52.3598775598299

x59 = 6.28318530717959

x60 = 25.1327412287183

x61 = 39.7935069454707

x62 = -10.471975511966

x63 = 46.0766922526503

x64 = 64.9262481741891

x65 = -94.2477796076938

x66 = 14.6607657167524

x67 = -60.7374579694027

x68 = -73.3038285837618

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