2*cos(x)+3*sin(x)=0

$$3 sin{left (x right )} + 2 cos{left (x right )} = 0$$

Дано уравнение
$$3 sin{left (x right )} + 2 cos{left (x right )} = 0$$
преобразуем:
$$frac{3 sin{left (x right )}}{cos{left (x right )}} = -2$$
или
$$3 tan{left (x right )} = -2$$
– это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 3

Ур-ние превратится в
$$tan{left (x right )} = frac{2}{3}$$
Это ур-ние преобразуется в
$$x = pi n + {atan}{left (frac{2}{3} right )}$$
Или
$$x = pi n + {atan}{left (frac{2}{3} right )}$$
, где n – любое целое число

$$x_{1} = 2 {atan}{left (frac{3}{2} + frac{sqrt{13}}{2} right )}$$

/ ____
|3 / 13 |
x2 = 2*atan|- – ——|
2 2 /

$$x_{2} = 2 {atan}{left (- frac{sqrt{13}}{2} + frac{3}{2} right )}$$

x1 = 93.6597770041000

x2 = 99.9429623113000

x3 = -44.5702997538000

x4 = -101.118967518000

x5 = -19.4375585251000

x6 = -47.7118924074000

x7 = -10.0127805643000

x8 = -0.588002603548000

x9 = 43.3942945467000

x10 = -69.7030409825000

x11 = -38.2871144466000

x12 = -97.9773748648000

x13 = -13.1543732179000

x14 = -28.8623364859000

x15 = -57.1366703682000

x16 = 2006.88970304000

x17 = -16.2959658715000

x18 = -6.87118791073000

x19 = 33.9695165859000

x20 = 40.2527018931000

x21 = 90.5181843506000

x22 = 24.5447386252000

x23 = 68.5270357754000

x24 = -25.7207438323000

x25 = 77.9518137362000

x26 = -82.2694115969000

x27 = -32.0039291394000

x28 = 8.83677535722000

x29 = 30.8279239324000

x30 = -60.2782630218000

x31 = 37.1111092395000

x32 = 27.6863312788000

x33 = -41.4287071002000

x34 = 62.2438504682000

x35 = 11.9783680108000

x36 = 74.8102210826000

x37 = 15.1199606644000

x38 = -72.8446336361000

x39 = 417.243820324000

x40 = 46.5358872003000

x41 = -85.4110042505000

x42 = 55.9606651611000

x43 = -66.5614483289000

x44 = 49.6774798539000

x45 = 81.0934063898000

x46 = -63.4198556753000

x47 = -88.5525969041000

x48 = -3.72959525714000

x49 = -53.9950777146000

x50 = -94.8357822112000

x51 = -50.8534850610000

x52 = -211.074710394000

x53 = -22.5791511787000

x54 = -35.1455217930000

x55 = 52.8190725075000

x56 = 18.2615533180000

x57 = 87.3765916970000

x58 = 5.69518270363000

x59 = -91.6941895577000

x60 = 65.3854431218000

x61 = 21.4031459716000

x62 = -79.1278189433000

x63 = 96.8013696577000

x64 = 59.1022578147000

x65 = 84.2349990434000

x66 = 2.55359005004000

x67 = 118.792518233000

x68 = 71.6686284290000

x69 = -75.9862262897000