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

Разделим обе части ур-ния на -1

Ур-ние превратится в
$$\sin{\left(t \right)} = -1$$
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 = -14.1371667858125

t2 = -7.85398119154045

t3 = -39.2699084145515

t4 = 4.71239022926564

t5 = -70.6858331259916

t6 = -51.8362786893284

t7 = -89.5353906059052

t8 = -76.9690203748894

t9 = 67.5442415586719

t10 = -58.1194639976905

t11 = -51.8362783335234

t12 = 73.8274274426229

t13 = -1.57079581340397

t14 = 36.1283159497235

t15 = -20.4203527465087

t16 = 86.3937984838325

t17 = 80.1106131368654

t18 = 17.2787591562062

t19 = -45.5530935911043

t20 = -58.1194639046052

t21 = 23.5619451518571

t22 = -89.535390750197

t23 = -32.9867232184024

t24 = -7.85398205280014

t25 = 80.1106122287081

t26 = 67.54424230971

t27 = 98.9601692809083

t28 = -58.1194645939029

t29 = 29.8451303231501

t30 = -1.57079643188553

t31 = -1.57079639503667

t32 = -70.6858343571487

t33 = 61.2610563112167

t34 = -95.8185758680502

t35 = 29.845130330036

t36 = -64.4026502975618

t37 = 98.9601690454399

t38 = 29.8451297031011

t39 = 61.2610571125526

t40 = 48.6946859012172

t41 = 92.6769837888103

t42 = 42.4115013353669

t43 = 36.1283150875497

t44 = 98.9601682515978

t45 = -83.2522042893833

t46 = 42.4115007162407

t47 = -39.2699076683741

t48 = -64.4026498988255

t49 = -7.85398149665124

t50 = -45.5530935025548

t51 = -14.1371674455661

t52 = 48.6946870830469

t53 = -20.4203520060805

t54 = 23.5619437708833

t55 = -83.2522048211133

t56 = 538.783139388541

t57 = -76.9690195738024

t58 = 48.6946873020308

t59 = -83.2522055723275

t60 = -51.8362791922783

t61 = -102.101761026058

t62 = 42.4115007274741

t63 = -14.1371668370864

t64 = 54.9778710948428

t65 = 80.1106130902139

t66 = -32.9867224188086

t67 = 36.1283157235346

t68 = 73.8274274830848

t69 = 17.2787599560783

t70 = 4.71238874329685

t71 = -95.8185763308148

t72 = 48.6946866365921

t73 = 10.9955747360645

t74 = -39.2699069219675

t75 = -89.5353901118113

t76 = -20.420353265929

t77 = -64.4026491641039

t78 = -26.7035379986821

t79 = 67.5442408278864

t80 = 86.3937978309099

t81 = 92.6769830592094

t82 = -70.6858351534454

t83 = -45.5530929624673

t84 = 54.9778718908148

t85 = 92.6769843439965

t86 = 10.9955739381756

t87 = -95.818575476176

t88 = 4.7123894841958

t89 = 73.8274268520838

t90 = 23.5619444059921

t91 = -26.7035372004893

t92 = 86.3937978869933

График