sin(t)=-1 (уравнение)

Найду корень уравнения: sin(t)=-1

Вы ввели

sin(t) = -1

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

Подробное решение

Дано уравнение
$$\sin{\left(t \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$t = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Или
$$t = 2 \pi n - \frac{\pi}{2}$$
$$t = 2 \pi n + \frac{3 \pi}{2}$$
, где n - любое целое число

Быстрый ответ

     -pi 
t1 = ----
      2  

$$t_{1} = - \frac{\pi}{2}$$

     3*pi
t2 = ----
      2  

$$t_{2} = \frac{3 \pi}{2}$$

Сумма и произведение корней

сумма

  pi   3*pi
- -- + ----
  2     2  

$$- \frac{\pi}{2} + \frac{3 \pi}{2}$$

=

pi

$$\pi$$

произведение

-pi  3*pi
----*----
 2    2  

$$- \frac{\pi}{2} \frac{3 \pi}{2}$$

=

     2
-3*pi 
------
  4   

$$- \frac{3 \pi^{2}}{4}$$

Численный ответ

t1 = -14.1371667858125

t2 = 36.1283159497235

t3 = -76.9690203748894

t4 = -32.9867224188086

t5 = -70.6858343571487

t6 = -58.1194645939029

t7 = -76.9690195738024

t8 = 80.1106131368654

t9 = 73.8274268520838

t10 = -45.5530935911043

t11 = 48.6946859012172

t12 = -95.818575476176

t13 = 42.4115013353669

t14 = 86.3937984838325

t15 = 10.9955747360645

t16 = 92.6769843439965

t17 = 86.3937978869933

t18 = -14.1371674455661

t19 = 61.2610571125526

t20 = -7.85398149665124

t21 = 98.9601692809083

t22 = -89.535390750197

t23 = -58.1194639046052

t24 = 23.5619444059921

t25 = 29.8451297031011

t26 = 23.5619451518571

t27 = 54.9778710948428

t28 = 17.2787591562062

t29 = -1.57079639503667

t30 = -39.2699076683741

t31 = -20.4203527465087

t32 = -70.6858351534454

t33 = 48.6946870830469

t34 = 36.1283150875497

t35 = 92.6769830592094

t36 = 29.845130330036

t37 = 538.783139388541

t38 = -39.2699084145515

t39 = 23.5619437708833

t40 = -70.6858331259916

t41 = 98.9601690454399

t42 = -95.8185758680502

t43 = -64.4026498988255

t44 = 17.2787599560783

t45 = 61.2610563112167

t46 = -64.4026491641039

t47 = -1.57079643188553

t48 = 48.6946873020308

t49 = 73.8274274426229

t50 = 80.1106130902139

t51 = -14.1371668370864

t52 = 48.6946866365921

t53 = 67.54424230971

t54 = -89.5353901118113

t55 = 67.5442415586719

t56 = -83.2522042893833

t57 = -58.1194639976905

t58 = 4.71238874329685

t59 = -7.85398119154045

t60 = 36.1283157235346

t61 = -45.5530929624673

t62 = 54.9778718908148

t63 = -32.9867232184024

t64 = -39.2699069219675

t65 = -51.8362786893284

t66 = 67.5442408278864

t67 = 98.9601682515978

t68 = -51.8362791922783

t69 = -26.7035372004893

t70 = 80.1106122287081

t71 = 86.3937978309099

t72 = -1.57079581340397

t73 = -64.4026502975618

t74 = -20.4203520060805

t75 = -89.5353906059052

t76 = -20.420353265929

t77 = 73.8274274830848

t78 = 4.71239022926564

t79 = 4.7123894841958

t80 = 42.4115007162407

t81 = -102.101761026058

t82 = -26.7035379986821

t83 = -45.5530935025548

t84 = 92.6769837888103

t85 = 29.8451303231501

t86 = 42.4115007274741

t87 = -83.2522055723275

t88 = -83.2522048211133

t89 = -7.85398205280014

t90 = 10.9955739381756

t91 = -51.8362783335234

t92 = -95.8185763308148

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