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sin(x)=-1/7

sin(x)=-1/7 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
sin(x) = -1/7
$$\sin{\left(x \right)} = - \frac{1}{7}$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(x \right)} = - \frac{1}{7}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{7} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{7} \right)} + \pi$$
O
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{7} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{7} \right)} + \pi$$
, donde n es cualquier número entero
Gráfica
Respuesta rápida [src]
x1 = pi + asin(1/7)
$$x_{1} = \operatorname{asin}{\left(\frac{1}{7} \right)} + \pi$$
x2 = -asin(1/7)
$$x_{2} = - \operatorname{asin}{\left(\frac{1}{7} \right)}$$
x2 = -asin(1/7)
Suma y producto de raíces [src]
suma
pi + asin(1/7) - asin(1/7)
$$- \operatorname{asin}{\left(\frac{1}{7} \right)} + \left(\operatorname{asin}{\left(\frac{1}{7} \right)} + \pi\right)$$
=
pi
$$\pi$$
producto
(pi + asin(1/7))*(-asin(1/7))
$$\left(\operatorname{asin}{\left(\frac{1}{7} \right)} + \pi\right) \left(- \operatorname{asin}{\left(\frac{1}{7} \right)}\right)$$
=
-(pi + asin(1/7))*asin(1/7)
$$- \left(\operatorname{asin}{\left(\frac{1}{7} \right)} + \pi\right) \operatorname{asin}{\left(\frac{1}{7} \right)}$$
-(pi + asin(1/7))*asin(1/7)
Respuesta numérica [src]
x1 = -2.99824508468443
x2 = 263.750435332637
x3 = -75.5415712550604
x4 = -94.3911271765992
x5 = 72.3999786014706
x6 = -69.2583859478808
x7 = 75.2548761172497
x8 = 94.1044320387884
x9 = -65.8300981564803
x10 = 37.5557642741722
x11 = -25.2760887976237
x12 = 47.2672373727523
x13 = 53.5504226799318
x14 = -81.82475656224
x15 = 97.532719830189
x16 = 43.8389495813517
x17 = -21.8478010062232
x18 = -90.9628393851986
x19 = -72.1132834636599
x20 = -56.6920153335216
x21 = -97.2460246923782
x22 = 81.5380614244293
x23 = 12.4230230454538
x24 = 28.4176814512135
x25 = 15.8513108368543
x26 = 59.8336079871114
x27 = -6.42653287608495
x28 = -44.1256447191625
x29 = 62.6885055028905
x30 = -40.6973569277619
x31 = -31.5592741048033
x32 = -15.5646156990436
x33 = 91.2495345230094
x34 = 9.56812552967475
x35 = -100.674312483779
x36 = -18.9929034904441
x37 = 24.989393659813
x38 = 68.9716908100701
x39 = 100.387617345968
x40 = 31.2725789669926
x41 = 22.1344961440339
x42 = -50.4088300263421
x43 = 84.9663492158298
x44 = -78.3964687708395
x45 = -59.5469128493007
x46 = -34.4141716205824
x47 = -62.9752006407012
x48 = -12.7097181832645
x49 = 18.7062083526334
x50 = 78.6831639086502
x51 = -103.529209999558
x52 = -0.143347568905365
x53 = 3.28494022249516
x54 = 298.594649659936
x55 = 40.9840520655727
x56 = 66.116793294291
x57 = 6.13983773827422
x58 = 56.4053201957109
x59 = 34.7008667583931
x60 = -28.1309863134028
x61 = -46.9805422349415
x62 = -9.28143039186401
x63 = -37.8424594119829
x64 = 87.8212467316089
x65 = -88.1079418694196
x66 = -84.6796540780191
x67 = 50.1221348885313
x68 = -53.2637275421211
x68 = -53.2637275421211
Gráfico
sin(x)=-1/7 la ecuación