sinx=0,35 (уравнение)

Найду корень уравнения: sinx=0,35

Вы ввели

sin(x) = 7/20

$$\sin{\left(x \right)} = \frac{7}{20}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{7}{20}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{7}{20} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{7}{20} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{7}{20} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{7}{20} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(7/20)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{7}{20} \right)}$$

x2 = asin(7/20)

$$x_{2} = \operatorname{asin}{\left(\frac{7}{20} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(7/20) + asin(7/20)

$$\operatorname{asin}{\left(\frac{7}{20} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{7}{20} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(7/20))*asin(7/20)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{7}{20} \right)}\right) \operatorname{asin}{\left(\frac{7}{20} \right)}$$

=

(pi - asin(7/20))*asin(7/20)

$$\left(\pi - \operatorname{asin}{\left(\frac{7}{20} \right)}\right) \operatorname{asin}{\left(\frac{7}{20} \right)}$$

Численный ответ

x1 = -24.7751701250728

x2 = -722.208739222007

x3 = -288.668953026615

x4 = -16.0655343715945

x5 = -5.92561420353408

x6 = 2.78402154994428

x7 = -18.4919848178933

x8 = 21.633577471483

x9 = -62.4742819681504

x10 = -97.7469433649291

x11 = 38.056682946723

x12 = 90.7486158504585

x13 = 100.888536018519

x14 = -43.6247260466116

x15 = 923.985811259045

x16 = 88.3221654041597

x17 = 78.1822452360993

x18 = -47.4814609074924

x19 = -3.4991637572353

x20 = 97.0318011576381

x21 = -28.6319049859536

x22 = 71.8990599289197

x23 = 12.9239417180047

x24 = -75.0406525825095

x25 = -91.4637580577495

x26 = -9.78234906441489

x27 = -85.1805727505699

x28 = -60.0478315218516

x29 = -12.2087995107137

x30 = 82.0389800969801

x31 = -31.0583554322524

x32 = -72.6142021362107

x33 = 84.4654305432789

x34 = -34.9150902931332

x35 = -37.341540739432

x36 = -100.173393811228

x37 = 65.6158746217401

x38 = 27.9167627786626

x39 = 25.4903123323639

x40 = 69.472609482621

x41 = -68.7574672753299

x42 = -49.9079113537912

x43 = 641.242472435963

x44 = 94.6053507113393

x45 = -56.1910966609708

x46 = 40.4831333930218

x47 = 53.049504007381

x48 = 34.1999480858422

x49 = -78.8973874433903

x50 = -53.764646214672

x51 = 15.3503921643035

x52 = 75.7557947898005

x53 = 50.6230535610822

x54 = 44.3398682539026

x55 = -41.1982756003128

x56 = -217.127464201341

x57 = 0.35757110364551

x58 = 9.06720685712387

x59 = 19.2071270251843

x60 = 452.746913220576

x61 = -81.3238378896891

x62 = 31.7734976395434

x63 = 6.6407564108251

x64 = -22.3487196787741

x65 = 46.7663187002014

x66 = -198.277908279802

x67 = 56.9062388682618

x68 = -66.3310168290312

x69 = -87.6070231968687

x70 = 446.463727913396

x71 = 63.1894241754414

x72 = -93.8902085040483

x73 = 59.3326893145606

График