sin2t=1 (уравнение)

Найду корень уравнения: sin2t=1

Вы ввели

sin(2*t) = 1

$$\sin{\left(2 t \right)} = 1$$

Подробное решение

Дано уравнение
$$\sin{\left(2 t \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$2 t = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$2 t = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Или
$$2 t = 2 \pi n + \frac{\pi}{2}$$
$$2 t = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$t_{1} = \pi n + \frac{\pi}{4}$$
$$t_{2} = \pi n + \frac{\pi}{4}$$

Быстрый ответ

     pi
t1 = --
     4 

$$t_{1} = \frac{\pi}{4}$$

Сумма и произведение корней

сумма

    pi
0 + --
    4 

$$0 + \frac{\pi}{4}$$

=

pi
--
4 

$$\frac{\pi}{4}$$

произведение

  pi
1*--
  4 

$$1 \frac{\pi}{4}$$

=

pi
--
4 

$$\frac{\pi}{4}$$

Численный ответ

t1 = 82.4668070362749

t2 = 7.06858323491875

t3 = 0.785397933202895

t4 = -65.1880477975749

t5 = -80.8960110535094

t6 = -46.3384918201522

t7 = -43.1968987801324

t8 = -62.0464545510179

t9 = -74.6128252689663

t10 = 91.8915852031867

t11 = 16.4933612990544

t12 = 38.4845098780771

t13 = 7.06858364655338

t14 = -52.621676693071

t15 = -14.9225649210104

t16 = -65.1880480738962

t17 = -62.0464548641931

t18 = 35.3429176094788

t19 = 13.3517690013813

t20 = -30.6305281172761

t21 = 88.7499922419838

t22 = 10.2101761576945

t23 = -14.9225653376224

t24 = 57.334066070126

t25 = -27.4889358588398

t26 = 19.6349542839773

t27 = 73.0420289540461

t28 = 66.7588436646782

t29 = -74.6128250890583

t30 = 25.9181398404781

t31 = -90.320788607123

t32 = 47.9092880421864

t33 = -24.3473428722772

t34 = -24.3473430701779

t35 = -77.754418173028

t36 = -2.35619429411883

t37 = -46.3384914504975

t38 = -87.1791967606238

t39 = 57.3340661848436

t40 = -80.8960106270747

t41 = -40.0553062823371

t42 = 85.6084000178882

t43 = 3.92699088042162

t44 = 101.316363152916

t45 = -21.2057506438029

t46 = -33.7721210085969

t47 = -52.6216765719183

t48 = 95.0331775275438

t49 = 95.0331779096874

t50 = 51.0508807796768

t51 = 41.6261028620108

t52 = -55.7632695910029

t53 = 63.6172514399813

t54 = 76.1836219129628

t55 = -2.35619439286547

t56 = -99.745566754733

t57 = -68.3296400287794

t58 = 60.4756584571505

t59 = 98.1747705006042

t60 = -84.0376034464448

t61 = -8.6393795270917

t62 = -96.6039738449592

t63 = -5.49778727991785

t64 = 73.0420293451081

t65 = -58.9048620578704

t66 = -96.6039736043971

t67 = 44.7676950874451

t68 = 35.3429175338589

t69 = -8.63937954158422

t70 = 32.2013247418177

t71 = 29.0597318077204

t72 = 79.3252147600926

t73 = -87.1791963743373

t74 = -49.4800844377116

t75 = -18.064157700815

t76 = 69.9004366227711

t77 = 25.9181394614117

t78 = -71.471233016533

t79 = -93.4623815953041

t80 = -58.9048624818554

t81 = 79.3252146099091

t82 = -43.1968992207295

t83 = -36.9137134891678

t84 = 29.0597322134693

t85 = -153.15264217109

t86 = 51.0508803807674

t87 = -30.6305280514717

t88 = -11.7809724257318

t89 = 13.3517690340018

t90 = -36.9137139098865

t91 = 54.192473326822

t92 = 22.7765465102862

График