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sint=-sqrt3/2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
            ___ 
         -\/ 3  
sin(t) = -------
            2   
$$\sin{\left(t \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(t \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$t = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
O
$$t = 2 \pi n - \frac{\pi}{3}$$
$$t = 2 \pi n + \frac{4 \pi}{3}$$
, donde n es cualquier número entero
Gráfica
Suma y producto de raíces [src]
suma
  pi   4*pi
- -- + ----
  3     3  
$$- \frac{\pi}{3} + \frac{4 \pi}{3}$$
=
pi
$$\pi$$
producto
-pi  4*pi
----*----
 3    3  
$$- \frac{\pi}{3} \frac{4 \pi}{3}$$
=
     2
-4*pi 
------
  9   
$$- \frac{4 \pi^{2}}{9}$$
-4*pi^2/9
Respuesta rápida [src]
     -pi 
t1 = ----
      3  
$$t_{1} = - \frac{\pi}{3}$$
     4*pi
t2 = ----
      3  
$$t_{2} = \frac{4 \pi}{3}$$
t2 = 4*pi/3
Respuesta numérica [src]
t1 = 30.3687289847013
t2 = -83.7758040957278
t3 = 36.6519142918809
t4 = 79.5870138909414
t5 = 55.5014702134197
t6 = -27.2271363311115
t7 = -64.9262481741891
t8 = -5606.69568910658
t9 = 16.7551608191456
t10 = 74.3510261349584
t11 = 60.7374579694027
t12 = -51.3126800086333
t13 = -58.6430628670095
t14 = -45.0294947014537
t15 = 99.4837673636768
t16 = 92.1533845053006
t17 = -19.8967534727354
t18 = -13.6135681655558
t19 = 23.0383461263252
t20 = 61.7846555205993
t21 = 11.5191730631626
t22 = 35.6047167406843
t23 = 29.3215314335047
t24 = 93.2005820564972
t25 = 80.634211442138
t26 = -1559.27715373173
t27 = -96.342174710087
t28 = 4.18879020478639
t29 = 54.4542726622231
t30 = 98.4365698124802
t31 = 67.0206432765823
t32 = -76.4454212373516
t33 = -38.7463093942741
t34 = -114.144533080429
t35 = 85.870199198121
t36 = -11851.1346868919
t37 = -14.6607657167524
t38 = -95.2949771588904
t39 = -57.5958653158129
t40 = 24.0855436775217
t41 = -2.0943951023932
t42 = 5.23598775598299
t43 = -32.4631240870945
t44 = -63.8790506229925
t45 = -26.1799387799149
t46 = -70.162235930172
t47 = -33.5103216382911
t48 = -39.7935069454707
t49 = -101.57816246607
t50 = 73.3038285837618
t51 = 17.8023583703422
t52 = -7.33038285837618
t53 = 49.2182849062401
t54 = -46.0766922526503
t55 = -90.0589894029074
t56 = -89.0117918517108
t57 = 393.746279249921
t58 = -1.0471975511966
t59 = 48.1710873550435
t60 = -20.943951023932
t61 = 68.0678408277789
t62 = 41.8879020478639
t63 = -8.37758040957278
t64 = 86.9173967493176
t65 = -71.2094334813686
t66 = 10.471975511966
t67 = -151.843644923507
t68 = -82.7286065445312
t69 = 42.9350995990605
t70 = -52.3598775598299
t71 = -77.4926187885482
t71 = -77.4926187885482