Sr Examen
4*sin(x+pi/4)-3=0 la ecuación
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Solución
Ha introducido
[src]
/ pi\
4*sin|x + --| - 3 = 0
\ 4 /
$$4 \sin{\left(x + \frac{\pi}{4} \right)} - 3 = 0$$
Solución detallada
Tenemos la ecuación
$$4 \sin{\left(x + \frac{\pi}{4} \right)} - 3 = 0$$
es la ecuación trigonométrica más simple
Obtenemos:
$$4 \sin{\left(x + \frac{\pi}{4} \right)} = 3$$
La ecuación se convierte en
$$\sin{\left(x + \frac{\pi}{4} \right)} = \frac{3}{4}$$
Esta ecuación se reorganiza en
$$x + \frac{\pi}{4} = 2 \pi n + \operatorname{asin}{\left(\frac{3}{4} \right)}$$
$$x + \frac{\pi}{4} = 2 \pi n - \operatorname{asin}{\left(\frac{3}{4} \right)} + \pi$$
O
$$x + \frac{\pi}{4} = 2 \pi n + \operatorname{asin}{\left(\frac{3}{4} \right)}$$
$$x + \frac{\pi}{4} = 2 \pi n - \operatorname{asin}{\left(\frac{3}{4} \right)} + \pi$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{4}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = 2 \pi n - \frac{\pi}{4} + \operatorname{asin}{\left(\frac{3}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{4} \right)} + \frac{3 \pi}{4}$$
$$4 \sin{\left(x + \frac{\pi}{4} \right)} - 3 = 0$$
es la ecuación trigonométrica más simple
Transportemos -3 al miembro derecho de la ecuación
cambiando el signo de -3
Obtenemos:
$$4 \sin{\left(x + \frac{\pi}{4} \right)} = 3$$
Dividamos ambos miembros de la ecuación en 4
La ecuación se convierte en
$$\sin{\left(x + \frac{\pi}{4} \right)} = \frac{3}{4}$$
Esta ecuación se reorganiza en
$$x + \frac{\pi}{4} = 2 \pi n + \operatorname{asin}{\left(\frac{3}{4} \right)}$$
$$x + \frac{\pi}{4} = 2 \pi n - \operatorname{asin}{\left(\frac{3}{4} \right)} + \pi$$
O
$$x + \frac{\pi}{4} = 2 \pi n + \operatorname{asin}{\left(\frac{3}{4} \right)}$$
$$x + \frac{\pi}{4} = 2 \pi n - \operatorname{asin}{\left(\frac{3}{4} \right)} + \pi$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{4}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = 2 \pi n - \frac{\pi}{4} + \operatorname{asin}{\left(\frac{3}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{4} \right)} + \frac{3 \pi}{4}$$
Suma y producto de raíces
[src]
suma
pi 3*pi - -- + asin(3/4) + -asin(3/4) + ---- 4 4
$$\left(- \frac{\pi}{4} + \operatorname{asin}{\left(\frac{3}{4} \right)}\right) + \left(- \operatorname{asin}{\left(\frac{3}{4} \right)} + \frac{3 \pi}{4}\right)$$
=
pi -- 2
$$\frac{\pi}{2}$$
producto
/ pi \ / 3*pi\ |- -- + asin(3/4)|*|-asin(3/4) + ----| \ 4 / \ 4 /
$$\left(- \frac{\pi}{4} + \operatorname{asin}{\left(\frac{3}{4} \right)}\right) \left(- \operatorname{asin}{\left(\frac{3}{4} \right)} + \frac{3 \pi}{4}\right)$$
=
2
2 3*pi
- asin (3/4) - ----- + pi*asin(3/4)
16
$$- \frac{3 \pi^{2}}{16} - \operatorname{asin}^{2}{\left(\frac{3}{4} \right)} + \pi \operatorname{asin}{\left(\frac{3}{4} \right)}$$
-asin(3/4)^2 - 3*pi^2/16 + pi*asin(3/4)
Respuesta rápida
[src]
pi
x1 = - -- + asin(3/4)
4
$$x_{1} = - \frac{\pi}{4} + \operatorname{asin}{\left(\frac{3}{4} \right)}$$
3*pi
x2 = -asin(3/4) + ----
4
$$x_{2} = - \operatorname{asin}{\left(\frac{3}{4} \right)} + \frac{3 \pi}{4}$$
x2 = -asin(3/4) + 3*pi/4
Respuesta numérica
[src]
x1 = -23.6246088175075
x2 = -8218.34371787532
x3 = 18.9122198371228
x4 = -29.9077941246871
x5 = 170049.63528592
x6 = 89.4727267117251
x7 = -43.9196332346731
x8 = -73.8900912749442
x9 = 62.8945169873799
x10 = -81.6187450777506
x11 = 1.50813241121086
x12 = 64.3399854830067
x13 = -80.1732765821238
x14 = -182.149709992624
x15 = -61.323720660585
x16 = 37.7617757586615
x17 = 76.9063560973659
x18 = 88.0272582160982
x19 = 81.7440729089187
x20 = 83.1895414045455
x21 = -12.5037066987751
x22 = 6.34584922276362
x23 = -25.0700773131343
x24 = -92.7396471964829
x25 = 31.478590451482
x26 = 25.1954051443024
x27 = 95.7559120189047
x28 = 100.593628830457
x29 = -67.6069059677646
x30 = -56.4860038490322
x31 = 75.4608876017391
x32 = 51.7736148686476
x33 = -99.0228325036625
x34 = 70.6231707901863
x35 = -207.282451221342
x36 = -62.7691891562118
x37 = -94.1851156921098
x38 = 32.9240589471088
x39 = 12.6290345299432
x40 = 44.0449610658411
x41 = -87.9019303849302
x42 = 20.3576883327496
x43 = -6.22052139159555
x44 = 39.2072442542884
x45 = 94.3104435232778
x46 = -48.7573500462258
x47 = 26.6408736399292
x48 = 0.0626639155840327
x49 = -69.0523744633914
x50 = -17.3414235103279
x51 = 50.3281463730207
x52 = -4.77505289596872
x53 = -86.4564618893033
x54 = 69.1777022945595
x55 = -11.0582382031483
x56 = -37.6364479274935
x57 = 14.07450302557
x58 = -75.335559770571
x59 = -36.1909794318667
x60 = 58.0568001758271
x61 = -31.3532626203139
x62 = 7.79131771839045
x63 = -42.4741647390462
x64 = -100.468300999289
x65 = 45.490429561468
x66 = -50.2028185418527
x67 = -55.0405353534054
x68 = -18.7868920059547
x69 = 56.6113316802003
x70 = 108.322282633264
x70 = 108.322282633264