sin(x)-cos((3*pi/2)-x)=sqrt(3)

Дано

$$\sin{\left (x \right )} — \cos{\left (- x + \frac{3 \pi}{2} \right )} = \sqrt{3}$$
Подробное решение
Дано уравнение
$$\sin{\left (x \right )} — \cos{\left (- x + \frac{3 \pi}{2} \right )} = \sqrt{3}$$
— это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$\sin{\left (x \right )} = \frac{\sqrt{3}}{2}$$
Это ур-ние преобразуется в
$$x = 2 \pi n + {asin}{\left (\frac{\sqrt{3}}{2} \right )}$$
$$x = 2 \pi n — {asin}{\left (\frac{\sqrt{3}}{2} \right )} + \pi$$
Или
$$x = 2 \pi n + \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{2 \pi}{3}$$
, где n — любое целое число

Ответ
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pi
x1 = —
3

$$x_{1} = \frac{\pi}{3}$$

2*pi
x2 = —-
3

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

x1 = -67.0206432766000

x2 = -36.6519142919000

x3 = 170.693200845000

x4 = -16.7551608191000

x5 = 20.9439510239000

x6 = -60.7374579694000

x7 = 195.825942074000

x8 = 71.2094334814000

x9 = -30.3687289847000

x10 = 58.6430628670000

x11 = 52.3598775598000

x12 = -104.719755120000

x13 = 624.129740513000

x14 = 38.7463093943000

x15 = 27.2271363311000

x16 = 90.0589894029000

x17 = 14.6607657168000

x18 = -29.3215314335000

x19 = 799.011731563000

x20 = -41.8879020479000

x21 = -61.7846555206000

x22 = -17.8023583703000

x23 = 82.7286065445000

x24 = -80.6342114421000

x25 = 13.6135681656000

x26 = 8.37758040957000

x27 = 7.33038285838000

x28 = 2.09439510239000

x29 = -79.5870138909000

x30 = 944.572191179000

x31 = 57.5958653158000

x32 = -85.8701991981000

x33 = -42.9350995991000

x34 = 26.1799387799000

x35 = 46.0766922527000

x36 = -520.457182945000

x37 = -10.4719755120000

x38 = -54.4542726622000

x39 = 76.4454212374000

x40 = -99.4837673637000

x41 = 39.7935069455000

x42 = -73.3038285838000

x43 = 32.4631240871000

x44 = -23.0383461263000

x45 = 77.4926187885000

x46 = -48.1710873550000

x47 = 64.9262481742000

x48 = -92.1533845053000

x49 = -11.5191730632000

x50 = -112.050137978000

x51 = 96.3421747101000

x52 = -35.6047167407000

x53 = -49.2182849062000

x54 = 51.3126800086000

x55 = 95.2949771589000

x56 = -98.4365698125000

x57 = 146.607657168000

x58 = -24.0855436775000

x59 = -4.18879020479000

x60 = 45.0294947015000

x61 = 209.439510239000

x62 = 83.7758040957000

x63 = -86.9173967493000

x64 = -93.2005820565000

x65 = 33.5103216383000

x66 = -68.0678408278000

x67 = -5.23598775598000

x68 = 89.0117918517000

x69 = 70.1622359302000

x70 = 19.8967534727000

x71 = 101.578162466000

x72 = 63.8790506230000

x73 = -55.5014702134000

x74 = -74.3510261350000

x75 = 1.04719755120000

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