sin4t=1 (уравнение)

Найду корень уравнения: sin4t=1

Вы ввели

sin(4*t) = 1

$$\sin{\left(4 t \right)} = 1$$

Подробное решение

Дано уравнение
$$\sin{\left(4 t \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$4 t = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$4 t = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Или
$$4 t = 2 \pi n + \frac{\pi}{2}$$
$$4 t = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$4$$
получим ответ:
$$t_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$
$$t_{2} = \frac{\pi n}{2} + \frac{\pi}{8}$$

Быстрый ответ

     pi
t1 = --
     8 

$$t_{1} = \frac{\pi}{8}$$

Сумма и произведение корней

сумма

    pi
0 + --
    8 

$$0 + \frac{\pi}{8}$$

=

pi
--
8 

$$\frac{\pi}{8}$$

произведение

  pi
1*--
  8 

$$1 \frac{\pi}{8}$$

=

pi
--
8 

$$\frac{\pi}{8}$$

Численный ответ

t1 = 23.9546440259598

t2 = -15.3152642379275

t3 = 9.81747676783862

t4 = -81.2887099089205

t5 = -73.4347283951574

t6 = 97.782071459868

t7 = 72.6493300240099

t8 = -29.4524312449951

t9 = 22.3838475810827

t10 = 69.5077373387294

t11 = 96.2112750487236

t12 = 9.81747715075509

t13 = -42.018801721698

t14 = 83.6449045156666

t15 = -228.943564806969

t16 = 80.5033116353485

t17 = -87.5718953117726

t18 = -12.1736714270123

t19 = 45.9457926074387

t20 = -86.00109889071

t21 = -67.1515431778245

t22 = -48.3019869255039

t23 = -84.430302507019

t24 = -78.1471171614871

t25 = 67.9369411885029

t26 = 0.392699002218603

t27 = 162.184720622203

t28 = -64.009950305697

t29 = -42.0188021311225

t30 = 17.6714587968444

t31 = 89.9280897692015

t32 = -57.7267650260013

t33 = 53.7997743057058

t34 = 75.7909228828866

t35 = 25.525440266285

t36 = -62.4391539454797

t37 = -93.8550803968028

t38 = -34.1648200049742

t39 = -43.5895981550743

t40 = -35.7356164448818

t41 = -20.0276531385131

t42 = -100.138265740044

t43 = 66.3661447392409

t44 = 39.6626073702294

t45 = 30.2378293001575

t46 = -87.5718952244412

t47 = -21.598449576501

t48 = -59.2975613554301

t49 = 52.2289778825359

t50 = -65.5807467334992

t51 = 72.6493300141926

t52 = 74.2201264653626

t53 = -12.1736719262543

t54 = -95.4258769697172

t55 = 6.67588432482476

t56 = -71.8639318172356

t57 = -79.7179136068893

t58 = 44.3749961600903

t59 = 58.5121630587909

t60 = 94.6404785931085

t61 = 1.96349544400331

t62 = -92.2842840752935

t63 = -37.3064127981981

t64 = -7.46128266944874

t65 = -26.3108383510529

t66 = 14.5298659063767

t67 = -56.1559685831317

t68 = 3.53429172010594

t69 = 8.24668071816113

t70 = 25.5254403437163

t71 = 47.5165888062105

t72 = -4.31968977692752

t73 = -13.7444678635051

t74 = 82.0741078307881

t75 = 52.2289777791699

t76 = 28.6670328896188

t77 = -51.4435798202399

t78 = 50.6581814561062

t79 = 36.5210144824622

t80 = 31.808625728328

t81 = 88.3572933185348

t82 = -18.4568568311997

t83 = 91.4988858631041

t84 = -70.2931355002572

t85 = 61.6537559431866

t86 = -40.4480053866604

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