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La ecuación:
Ecuación (x-3)*(x+2)=0
Ecuación (11x+14)-(5x-8)=25
Ecuación z^2-6*z+10=0
Ecuación 4/(x-4)=-5
Expresar {x} en función de y en la ecuación:
-7*x-13*y=5
15*x+1*y=19
7*x-1*y=-7
-11*x-14*y=-3
Expresiones idénticas
3sin(3x)+ dos /tan(3x/ dos)= cinco
3 seno de (3x) más 2 dividir por tangente de (3x dividir por 2) es igual a 5
3 seno de (3x) más dos dividir por tangente de (3x dividir por dos) es igual a cinco
3sin3x+2/tan3x/2=5
3sin(3x)+2 dividir por tan(3x dividir por 2)=5
Expresiones semejantes
3sin(3x)-2/tan(3x/2)=5
Expresiones con funciones
Tangente tan
tan(x-pi/6)=1/(sqrt(3))
tan(x)=2/3
tan(x-pi/3)=1
tan(x/2-pi/5)=1
tan(2*x)+cot(3*x)=8

3sin(3x)+2/tan(3x/2)=5 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

                2        
3*sin(3*x) + -------- = 5
                /3*x\    
             tan|---|    
                \ 2 /

$$3 \sin{\left(3 x \right)} + \frac{2}{\tan{\left(\frac{3 x}{2} \right)}} = 5$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

         /    /         ____\\         /    /         ____\\       /    /         ____\\         /    /         ____\\
         |    |3    I*\/ 31 ||         |    |3    I*\/ 31 ||       |    |3    I*\/ 31 ||         |    |3    I*\/ 31 ||
     2*re|atan|-- - --------||   2*I*im|atan|-- - --------||   2*re|atan|-- + --------||   2*I*im|atan|-- + --------||
pi       \    \10      10   //         \    \10      10   //       \    \10      10   //         \    \10      10   //
-- + ------------------------- + --------------------------- + ------------------------- + ---------------------------
6                3                            3                            3                            3

$$\left(\frac{\pi}{6} + \left(\frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{10} - \frac{\sqrt{31} i}{10} \right)}\right)}}{3} + \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{10} - \frac{\sqrt{31} i}{10} \right)}\right)}}{3}\right)\right) + \left(\frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{31} i}{10} \right)}\right)}}{3} + \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{31} i}{10} \right)}\right)}}{3}\right)$$

         /    /         ____\\       /    /         ____\\         /    /         ____\\         /    /         ____\\
         |    |3    I*\/ 31 ||       |    |3    I*\/ 31 ||         |    |3    I*\/ 31 ||         |    |3    I*\/ 31 ||
     2*re|atan|-- - --------||   2*re|atan|-- + --------||   2*I*im|atan|-- - --------||   2*I*im|atan|-- + --------||
pi       \    \10      10   //       \    \10      10   //         \    \10      10   //         \    \10      10   //
-- + ------------------------- + ------------------------- + --------------------------- + ---------------------------
6                3                           3                            3                             3

$$\frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{10} - \frac{\sqrt{31} i}{10} \right)}\right)}}{3} + \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{31} i}{10} \right)}\right)}}{3} + \frac{\pi}{6} + \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{10} - \frac{\sqrt{31} i}{10} \right)}\right)}}{3} + \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{31} i}{10} \right)}\right)}}{3}$$

producto

   /    /    /         ____\\         /    /         ____\\\ /    /    /         ____\\         /    /         ____\\\
   |    |    |3    I*\/ 31 ||         |    |3    I*\/ 31 ||| |    |    |3    I*\/ 31 ||         |    |3    I*\/ 31 |||
   |2*re|atan|-- - --------||   2*I*im|atan|-- - --------||| |2*re|atan|-- + --------||   2*I*im|atan|-- + --------|||
pi |    \    \10      10   //         \    \10      10   //| |    \    \10      10   //         \    \10      10   //|
--*|------------------------- + ---------------------------|*|------------------------- + ---------------------------|
6  \            3                            3             / \            3                            3             /

$$\frac{\pi}{6} \left(\frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{10} - \frac{\sqrt{31} i}{10} \right)}\right)}}{3} + \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{10} - \frac{\sqrt{31} i}{10} \right)}\right)}}{3}\right) \left(\frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{31} i}{10} \right)}\right)}}{3} + \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{31} i}{10} \right)}\right)}}{3}\right)$$

     /    /    /         ____\\     /    /         ____\\\ /    /    /         ____\\     /    /         ____\\\
     |    |    |3    I*\/ 31 ||     |    |3    I*\/ 31 ||| |    |    |3    I*\/ 31 ||     |    |3    I*\/ 31 |||
2*pi*|I*im|atan|-- - --------|| + re|atan|-- - --------|||*|I*im|atan|-- + --------|| + re|atan|-- + --------|||
     \    \    \10      10   //     \    \10      10   /// \    \    \10      10   //     \    \10      10   ///
----------------------------------------------------------------------------------------------------------------
                                                       27

$$\frac{2 \pi \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{10} - \frac{\sqrt{31} i}{10} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{10} - \frac{\sqrt{31} i}{10} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{31} i}{10} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{31} i}{10} \right)}\right)}\right)}{27}$$

2*pi*(i*im(atan(3/10 - i*sqrt(31)/10)) + re(atan(3/10 - i*sqrt(31)/10)))*(i*im(atan(3/10 + i*sqrt(31)/10)) + re(atan(3/10 + i*sqrt(31)/10)))/27

Respuesta rápida [src]

     pi
x1 = --
     6

$$x_{1} = \frac{\pi}{6}$$

         /    /         ____\\         /    /         ____\\
         |    |3    I*\/ 31 ||         |    |3    I*\/ 31 ||
     2*re|atan|-- - --------||   2*I*im|atan|-- - --------||
         \    \10      10   //         \    \10      10   //
x2 = ------------------------- + ---------------------------
                 3                            3

$$x_{2} = \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{10} - \frac{\sqrt{31} i}{10} \right)}\right)}}{3} + \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{10} - \frac{\sqrt{31} i}{10} \right)}\right)}}{3}$$

         /    /         ____\\         /    /         ____\\
         |    |3    I*\/ 31 ||         |    |3    I*\/ 31 ||
     2*re|atan|-- + --------||   2*I*im|atan|-- + --------||
         \    \10      10   //         \    \10      10   //
x3 = ------------------------- + ---------------------------
                 3                            3

$$x_{3} = \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{31} i}{10} \right)}\right)}}{3} + \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{31} i}{10} \right)}\right)}}{3}$$

x3 = 2*re(atan(3/10 + sqrt(31)*i/10))/3 + 2*i*im(atan(3/10 + sqrt(31)*i/10))/3

Respuesta numérica [src]

x1 = 82.2050077689329

x2 = 2.61799387799149

x3 = -70.6858347057703

x4 = 61.261056745001

x5 = -18.3259571459405

x6 = 44.5058959258554

x7 = 21.4675497995303

x8 = 42.4115008234622

x9 = 96.8657734856853

x10 = 98.9601685880785

x11 = -89.5353906273091

x12 = -49.7418836818384

x13 = 25.6563400043166

x14 = -51.8362787842316

x15 = -83.2522053201295

x16 = -14.1371669411541

x17 = -85.3466004225227

x18 = 92.6769832808989

x19 = 48.6946861306418

x20 = 67.5442420521806

x21 = -47.6474885794452

x22 = 71.733032256967

x23 = 23.5619449019235

x24 = -79.0634151153431

x25 = 38.2227106186758

x26 = -68.5914396033772

x27 = 6.80678408277789

x28 = 59.1666616426078

x29 = 88.4881930761125

x30 = 34.0339204138894

x31 = -62.3082542961976

x32 = -64.4026493985908

x33 = 17.2787595947439

x34 = -16.2315620435473

x35 = -93.7241808320955

x36 = 63.3554518473942

x37 = 75.9218224617533

x38 = -37.1755130674792

x39 = 69.6386371545737

x40 = -1.5707963267949

x41 = 90.5825881785057

x42 = 86.3937979737193

x43 = -60.2138591938044

x44 = -72.7802298081635

x45 = -43.4586983746588

x46 = -87.4409955249159

x47 = -91.6297857297023

x48 = 15.1843644923507

x49 = 36.1283155162826

x50 = 50.789081233035

x51 = -22.5147473507269

x52 = 27.7507351067098

x53 = -12.0427718387609

x54 = 80.1106126665397

x55 = 8.90117918517108

x56 = -56.025068989018

x57 = -74.8746249105567

x58 = 78.0162175641465

x59 = -24.60914245312

x60 = 94.7713783832921

x61 = 73.8274273593601

x62 = 46.6002910282486

x63 = -58.1194640914112

x64 = -9.94837673636768

x65 = -20.4203522483337

x66 = -41.3643032722656

x67 = 52.8834763354282

x68 = 54.9778714378214

x69 = -100.007366139275

x70 = -95.8185759344887

x71 = 29.845130209103

x72 = -81.1578102177363

x73 = 19.3731546971371

x74 = -30.8923277602996

x75 = 40.317105721069

x76 = -97.9129710368819

x77 = -35.081117965086

x78 = -53.9306738866248

x79 = -28.7979326579064

x80 = 31.9395253114962

x81 = -3.66519142918809

x82 = 84.2994028713261

x83 = 65.4498469497874

x84 = -26.7035375555132

x85 = -66.497044500984

x86 = 13.0899693899575

x87 = -45.553093477052

x88 = -7.85398163397448

x89 = -5.75958653158129

x89 = -5.75958653158129

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Expresiones idénticas

Expresiones semejantes

Expresiones con funciones

3sin(3x)+2/tan(3x/2)=5 la ecuación

Solución numérica:

Solución