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cosx=-15/16 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
         -15 
cos(x) = ----
          16 
$$\cos{\left(x \right)} = - \frac{15}{16}$$
Solución detallada
Tenemos la ecuación
$$\cos{\left(x \right)} = - \frac{15}{16}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(- \frac{15}{16} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{15}{16} \right)}$$
O
$$x = \pi n + \operatorname{acos}{\left(- \frac{15}{16} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{15}{16} \right)}$$
, donde n es cualquier número entero
Gráfica
Respuesta rápida [src]
           /-15 \       
x1 = - acos|----| + 2*pi
           \ 16 /       
$$x_{1} = - \operatorname{acos}{\left(- \frac{15}{16} \right)} + 2 \pi$$
         /-15 \
x2 = acos|----|
         \ 16 /
$$x_{2} = \operatorname{acos}{\left(- \frac{15}{16} \right)}$$
x2 = acos(-15/16)
Suma y producto de raíces [src]
suma
      /-15 \              /-15 \
- acos|----| + 2*pi + acos|----|
      \ 16 /              \ 16 /
$$\operatorname{acos}{\left(- \frac{15}{16} \right)} + \left(- \operatorname{acos}{\left(- \frac{15}{16} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
producto
/      /-15 \       \     /-15 \
|- acos|----| + 2*pi|*acos|----|
\      \ 16 /       /     \ 16 /
$$\left(- \operatorname{acos}{\left(- \frac{15}{16} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{15}{16} \right)}$$
=
/      /-15 \       \     /-15 \
|- acos|----| + 2*pi|*acos|----|
\      \ 16 /       /     \ 16 /
$$\left(- \operatorname{acos}{\left(- \frac{15}{16} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{15}{16} \right)}$$
(-acos(-15/16) + 2*pi)*acos(-15/16)
Respuesta numérica [src]
x1 = -122.166692288312
x2 = -9.06935675907916
x3 = -65.6180245236954
x4 = 90.7507657524138
x5 = -34.2020979877975
x6 = 97.7447934629738
x7 = -78.8952375414351
x8 = -84.4675804452342
x9 = -47.4793110055371
x10 = 53.7624963127167
x11 = -22.3465697768188
x12 = 84.4675804452342
x13 = 9.06935675907916
x14 = 15.3525420662587
x15 = 72.6120522342555
x16 = -28.6297550839984
x17 = 40.4852832949771
x18 = -59.3348392165158
x19 = 34.2020979877975
x20 = -27.9189126806179
x21 = -41.1961256983575
x22 = -90.7507657524138
x23 = 27.9189126806179
x24 = 53.0516539093363
x25 = 21.6357273734383
x26 = 3.49701385528002
x27 = -15.3525420662587
x28 = 66.3288669270759
x29 = -53.0516539093363
x30 = 22.3465697768188
x31 = -91.4616081557942
x32 = -72.6120522342555
x33 = -78.1843951380546
x34 = -53.7624963127167
x35 = 34.9129403911779
x36 = -66.3288669270759
x37 = 91.4616081557942
x38 = 60.0456816198963
x39 = 9.7801991624596
x40 = 78.8952375414351
x41 = 41.1961256983575
x42 = -97.0339510595934
x43 = 78.1843951380546
x44 = 47.4793110055371
x45 = 85.1784228486146
x46 = -3.49701385528002
x47 = 46.7684686021567
x48 = 65.6180245236954
x49 = -40.4852832949771
x50 = -97.7447934629738
x51 = -21.6357273734383
x52 = 59.3348392165158
x53 = 2.78617145189957
x54 = -85.1784228486146
x55 = -60.0456816198963
x56 = 71.901209830875
x57 = -2.78617145189957
x58 = -46.7684686021567
x59 = -34.9129403911779
x60 = -16.0633844696392
x61 = 16.0633844696392
x62 = 97.0339510595934
x63 = 28.6297550839984
x64 = -9.7801991624596
x65 = -71.901209830875
x65 = -71.901209830875