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- La ecuación:
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Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
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Ecuación x^2-14*x+33=0
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Ecuación x+18=8
- Expresar {x} en función de y en la ecuación:
- 12*x+1*y=15
- -17*x-12*y=-9
- 18*x+17*y=-14
- 16*x-17*y=-15
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Expresiones idénticas
- log(sin(x))- tres *cos(x)= cero
- logaritmo de ( seno de (x)) menos 3 multiplicar por coseno de (x) es igual a 0
- logaritmo de ( seno de (x)) menos tres multiplicar por coseno de (x) es igual a cero
- log(sin(x))-3cos(x)=0
- logsinx-3cosx=0
- log(sin(x))-3*cos(x)=O
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Expresiones semejantes
- log(sin(x))+3*cos(x)=0
- log(sinx)-3*cosx=0
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Expresiones con funciones
- Logaritmo log
- log^24x−log4x^3+2=0
- log(4^x-b,2)=0
- log(1/6)*(x-5)=x+1
- log_2(3)=log_x(x^(2)-1)
- log12x^2-8x+16(log(12))=0
- Seno sin
- sin(pi*x/6)=-1
- sin(x)=4/5
- sin(x)+cos(x)=0
- sin(x)=1
- sin(2x)-cos(x)=0
- Coseno cos
- cos(x)^(2)=cos(x)
- cos^2(x-1)=0
- cos^2(x)=cos(2pi/x)
- cos^23x-sin^(2)3x=0
- cos=-√2/2
log(sin(x))-3*cos(x)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
log(sin(x)) - 3*cos(x) = 0
$$\log{\left(\sin{\left(x \right)} \right)} - 3 \cos{\left(x \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$\log{\left(\sin{\left(x \right)} \right)} - 3 \cos{\left(x \right)} = 0$$
cambiamos
$$\log{\left(\sin{\left(x \right)} \right)} - 3 \cos{\left(x \right)} = 0$$
$$\log{\left(\sin{\left(x \right)} \right)} - 3 \cos{\left(x \right)} = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Tenemos la ecuación
$$\log{\left(w \right)} - 3 \cos{\left(x \right)} = 0$$
$$\log{\left(w \right)} = 3 \cos{\left(x \right)}$$
Es la ecuación de la forma:
Por definición log
entonces
$$w = e^{\frac{3 \cos{\left(x \right)}}{1}}$$
simplificamos
$$w = e^{3 \cos{\left(x \right)}}$$
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
$$\log{\left(\sin{\left(x \right)} \right)} - 3 \cos{\left(x \right)} = 0$$
cambiamos
$$\log{\left(\sin{\left(x \right)} \right)} - 3 \cos{\left(x \right)} = 0$$
$$\log{\left(\sin{\left(x \right)} \right)} - 3 \cos{\left(x \right)} = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Tenemos la ecuación
$$\log{\left(w \right)} - 3 \cos{\left(x \right)} = 0$$
$$\log{\left(w \right)} = 3 \cos{\left(x \right)}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$w = e^{\frac{3 \cos{\left(x \right)}}{1}}$$
simplificamos
$$w = e^{3 \cos{\left(x \right)}}$$
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
Respuesta numérica
[src]
x1 = 36.2120297547417 + 0.902955270269943*i
x2 = 7.85398163397448
x3 = -89.45167638885 + 0.902955270269943*i
x4 = -29.845130209103
x5 = -51.7525645457725 + 0.902955270269943*i
x6 = -67.5442420521806
x7 = 4.79610321884376 + 0.902955270269943*i
x8 = 64.4026493985908
x9 = -36.1283155162826
x10 = -83.1684910816705 + 0.902955270269943*i
x11 = -92.6769832808989
x12 = 83.2522053201295
x13 = -42.4115008234622
x14 = -61.261056745001
x15 = 29.9288444475621 + 0.902955270269943*i
x16 = -7.77026739551541 + 0.902955270269943*i
x17 = -98.9601685880785
x18 = -64.3189351601317 + 0.902955270269943*i
x19 = 11.0792885260233 + 0.902955270269943*i
x20 = -28.3243287495039
x21 = 32.9867228626928
x22 = 26.7035375555132
x23 = -95.7348616960296 + 0.902955270269943*i
x24 = -4.71238898038469
x25 = 95.8185759344887
x26 = -17.2787595947439
x27 = -10.9955742875643
x28 = 42.4952150619213 + 0.902955270269943*i
x29 = 28.2243390151123
x30 = -86.3937979737193
x31 = -45.4693792385929 + 0.902955270269943*i
x32 = -48.6946861306418
x33 = 76.9690200129499
x34 = 45.553093477052
x35 = 61.34477098346 + 0.902955270269943*i
x36 = -80.1106126665397
x37 = 23.6456591403825 + 0.902955270269943*i
x38 = -76.8853057744909 + 0.902955270269943*i
x39 = 72.2066361653694
x40 = 14.1371669411541
x41 = -58.0357498529521 + 0.902955270269943*i
x42 = 73.9111415978192 + 0.902955270269943*i
x43 = 92.760697519358 + 0.902955270269943*i
x44 = -66.0234405925815
x45 = 55.0615856762805 + 0.902955270269943*i
x46 = -70.6021204673113 + 0.902955270269943*i
x47 = 86.4775122121784 + 0.902955270269943*i
x48 = 80.1943269049988 + 0.902955270269943*i
x49 = -15.7579581351448
x50 = 70.6858347057703
x51 = -1.48708208833582 + 0.902955270269943*i
x52 = -59.7402552854019
x53 = -26.6198233170542 + 0.902955270269943*i
x54 = -20.3366380098746 + 0.902955270269943*i
x55 = 51.8362787842316
x56 = 20.4203522483337
x57 = 1.5707963267949
x58 = 89.5353906273091
x59 = -14.053452702695 + 0.902955270269943*i
x60 = 58.1194640914112
x61 = -54.9778714378214
x62 = 48.7784003691009 + 0.902955270269943*i
x63 = 17.3624738332029 + 0.902955270269943*i
x64 = 99.0438828265376 + 0.902955270269943*i
x65 = 39.2699081698724
x66 = -32.9030086242338 + 0.902955270269943*i
x67 = -39.1861939314133 + 0.902955270269943*i
x68 = 67.6279562906396 + 0.902955270269943*i
x69 = -23.5619449019235
x70 = -73.8274273593601
x70 = -73.8274273593601