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
0 - -- + ----
    2     2  

$$\left(- \frac{\pi}{2} + 0\right) + \frac{3 \pi}{2}$$

=

pi

$$\pi$$

произведение

  -pi  3*pi
1*----*----
   2    2  

$$\frac{3 \pi}{2} \cdot 1 \left(- \frac{\pi}{2}\right)$$

=

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

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

Численный ответ

t1 = -7.85398149665124

t2 = -51.8362783335234

t3 = 4.71239022926564

t4 = 67.54424230971

t5 = 23.5619451518571

t6 = -70.6858351534454

t7 = 10.9955739381756

t8 = -45.5530935911043

t9 = 29.8451297031011

t10 = 23.5619444059921

t11 = -58.1194639976905

t12 = 67.5442415586719

t13 = 98.9601682515978

t14 = 98.9601692809083

t15 = 42.4115007274741

t16 = 73.8274268520838

t17 = -64.4026498988255

t18 = -95.8185758680502

t19 = -39.2699076683741

t20 = -83.2522042893833

t21 = 48.6946859012172

t22 = -76.9690203748894

t23 = -95.8185763308148

t24 = -7.85398119154045

t25 = 73.8274274426229

t26 = 48.6946873020308

t27 = -83.2522055723275

t28 = -89.5353906059052

t29 = -45.5530929624673

t30 = 61.2610563112167

t31 = -7.85398205280014

t32 = 10.9955747360645

t33 = 61.2610571125526

t34 = 17.2787591562062

t35 = -51.8362791922783

t36 = 86.3937978869933

t37 = -1.57079643188553

t38 = -89.535390750197

t39 = -64.4026491641039

t40 = -58.1194645939029

t41 = 42.4115013353669

t42 = -51.8362786893284

t43 = 86.3937984838325

t44 = 80.1106130902139

t45 = -20.420353265929

t46 = 92.6769837888103

t47 = 36.1283159497235

t48 = 80.1106131368654

t49 = -1.57079639503667

t50 = -39.2699084145515

t51 = 92.6769843439965

t52 = 4.7123894841958

t53 = 29.845130330036

t54 = -14.1371668370864

t55 = 48.6946870830469

t56 = -76.9690195738024

t57 = 67.5442408278864

t58 = -26.7035379986821

t59 = 73.8274274830848

t60 = -14.1371674455661

t61 = 86.3937978309099

t62 = -70.6858343571487

t63 = 36.1283150875497

t64 = 538.783139388541

t65 = -14.1371667858125

t66 = -32.9867232184024

t67 = -58.1194639046052

t68 = -70.6858331259916

t69 = 4.71238874329685

t70 = 23.5619437708833

t71 = -26.7035372004893

t72 = -95.818575476176

t73 = 54.9778710948428

t74 = -45.5530935025548

t75 = -32.9867224188086

t76 = -89.5353901118113

t77 = -20.4203527465087

t78 = 98.9601690454399

t79 = -20.4203520060805

t80 = -1.57079581340397

t81 = 17.2787599560783

t82 = -83.2522048211133

t83 = 54.9778718908148

t84 = -64.4026502975618

t85 = 29.8451303231501

t86 = 48.6946866365921

t87 = 80.1106122287081

t88 = -39.2699069219675

t89 = 42.4115007162407

t90 = -102.101761026058

t91 = 92.6769830592094

t92 = 36.1283157235346

График