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sin(t)=-(1/2)*sqrt(2) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
            ___ 
         -\/ 2  
sin(t) = -------
            2   
$$\sin{\left(t \right)} = - \frac{\sqrt{2}}{2}$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(t \right)} = - \frac{\sqrt{2}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$t = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
O
$$t = 2 \pi n - \frac{\pi}{4}$$
$$t = 2 \pi n + \frac{5 \pi}{4}$$
, donde n es cualquier número entero
Gráfica
Respuesta rápida [src]
     -pi 
t1 = ----
      4  
$$t_{1} = - \frac{\pi}{4}$$
     5*pi
t2 = ----
      4  
$$t_{2} = \frac{5 \pi}{4}$$
t2 = 5*pi/4
Suma y producto de raíces [src]
suma
  pi   5*pi
- -- + ----
  4     4  
$$- \frac{\pi}{4} + \frac{5 \pi}{4}$$
=
pi
$$\pi$$
producto
-pi  5*pi
----*----
 4    4  
$$- \frac{\pi}{4} \frac{5 \pi}{4}$$
=
     2
-5*pi 
------
  16  
$$- \frac{5 \pi^{2}}{16}$$
-5*pi^2/16
Respuesta numérica [src]
t1 = 73.0420291959627
t2 = -96.6039740978861
t3 = -8.63937979737193
t4 = -0.785398163397448
t5 = -71.4712328691678
t6 = -38.484510006475
t7 = 3.92699081698724
t8 = -215482.625507887
t9 = -33.7721210260903
t10 = 18.0641577581413
t11 = 24.3473430653209
t12 = -40.0553063332699
t13 = -58.9048622548086
t14 = 80.8960108299372
t15 = -101.316363078271
t16 = -84.037603483527
t17 = -704.502152567511
t18 = 99.7455667514759
t19 = -69.9004365423729
t20 = 66.7588438887831
t21 = -830.165858711103
t22 = 87.1791961371168
t23 = -19.6349540849362
t24 = 49.4800842940392
t25 = 30.6305283725005
t26 = -2865.91789823729
t27 = -27.4889357189107
t28 = -13.3517687777566
t29 = 85.6083998103219
t30 = 54.1924732744239
t31 = -128.019900633784
t32 = 98.174770424681
t33 = -82.4668071567321
t34 = -63.6172512351933
t35 = 10.2101761241668
t36 = -21.2057504117311
t37 = 36.9137136796801
t38 = 41.6261026600648
t39 = 11.7809724509617
t40 = 35.3429173528852
t41 = -88.7499924639117
t42 = -76.1836218495525
t43 = 652.665873783279
t44 = 62.0464549083984
t45 = 68.329640215578
t46 = -32.2013246992954
t47 = -90.3207887907066
t48 = -371.493331286993
t49 = 91.8915851175014
t50 = -7.06858347057703
t51 = 55.7632696012188
t52 = -2.35619449019234
t53 = -65.1880475619882
t54 = 22.776546738526
t55 = 79.3252145031423
t56 = -46.3384916404494
t57 = -95.0331777710912
t58 = 29.0597320457056
t59 = 5.49778714378214
t60 = 43.1968989868597
t61 = -57.3340659280137
t62 = -52.621676947629
t63 = -14.9225651045515
t64 = 47.9092879672443
t65 = 60.4756585816035
t66 = 16.4933614313464
t67 = -25.9181393921158
t68 = 93.4623814442964
t69 = 74.6128255227576
t70 = -51.0508806208341
t71 = -77.7544181763474
t72 = -44.7676953136546
t72 = -44.7676953136546