Sr Examen

Lang:

tan(x+pi/6)=1 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Ha introducido [src]

   /    pi\    
tan|x + --| = 1
   \    6 /

\tan{\left(x + \frac{\pi}{6} \right)} = 1

Simplificar

Solución detallada

Tenemos la ecuación

\tan{\left(x + \frac{\pi}{6} \right)} = 1

es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en

x + \frac{\pi}{6} = \pi n + \operatorname{atan}{\left(1 \right)}

x + \frac{\pi}{6} = \pi n + \frac{\pi}{4}

, donde n es cualquier número entero
Transportemos

\frac{\pi}{6}

al miembro derecho de la ecuación
con el signo opuesto, en total:

x = \pi n + \frac{\pi}{12}

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

pi
--
12

\frac{\pi}{12}

pi
--
12

\frac{\pi}{12}

producto

pi
--
12

\frac{\pi}{12}

pi
--
12

\frac{\pi}{12}

pi/12

Respuesta rápida [src]

     pi
x1 = --
     12

x_{1} = \frac{\pi}{12}

x1 = pi/12

Respuesta numérica [src]

x1 = 97.6511716490827

x2 = 25.3945406165175

x3 = 3.40339204138894

x4 = -56.2868683768171

x5 = 72.5184304203644

x6 = -28.012534494509

x7 = 78.801615727544

x8 = 6.54498469497874

x9 = -97.1275728734844

x10 = -75.1364242983559

x11 = -90.8443875663049

x12 = -12.30457122656

x13 = -62.5700536839967

x14 = -9.16297857297023

x15 = -24.8709418409192

x16 = -65.7116463375865

x17 = 19.1113553093379

x18 = -84.5612022591253

x19 = 0.261799387799149

x20 = 53.6688744988256

x21 = 28.5361332701073

x22 = 81.9432083811338

x23 = -87.7027949127151

x24 = 69.3768377667746

x25 = 85.0848010347236

x26 = -15.4461638801498

x27 = -43.720497762458

x28 = -59.4284610304069

x29 = -34.2957198016886

x30 = -37.4373124552784

x31 = -68.8532389911763

x32 = 44.2440965380563

x33 = 59.9520598060052

x34 = -31.1541271480988

x35 = -21.7293491873294

x36 = -53.1452757232273

x37 = 41.1025038844665

x38 = -100.269165527074

x39 = 94.5095789954929

x40 = -18.5877565337396

x41 = 66.2352451131848

x42 = -46.8620904160477

x43 = 56.8104671524154

x44 = 47.3856891916461

x45 = -71.9948316447661

x46 = 9.68657734856853

x47 = 63.093652459595

x48 = -81.4196096055355

x49 = -78.2780169519457

x50 = -6.02138591938044

x51 = -50.0036830696375

x52 = 37.9609112308767

x53 = 100.792764302673

x54 = 88.2263936883134

x55 = 31.6777259236971

x56 = 34.8193185772869

x57 = 15.9697626557481

x58 = 91.3679863419031

x59 = 22.2529479629277

x60 = -40.5789051088682

x61 = 75.6600230739542

x62 = -93.9859802198946

x63 = 12.8281700021583

x64 = 50.5272818452358

x65 = -2.87979326579064

x65 = -2.87979326579064