Sr Examen

Otras calculadoras

-sin(a)+cos(pi/(a+2))=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
             /  pi \    
-sin(a) + cos|-----| = 0
             \a + 2/    
$$- \sin{\left(a \right)} + \cos{\left(\frac{\pi}{a + 2} \right)} = 0$$
Gráfica
Suma y producto de raíces [src]
suma
                       __________________           __________________     
                      /        2                   /        2              
     pi        pi   \/  16 + pi  + 24*pi         \/  16 + pi  + 24*pi    pi
-2 + -- + -1 + -- + --------------------- + -1 - --------------------- + --
     2         4              4                            4             4 
$$\left(- \frac{\sqrt{\pi^{2} + 16 + 24 \pi}}{4} - 1 + \frac{\pi}{4}\right) + \left(\left(-2 + \frac{\pi}{2}\right) + \left(-1 + \frac{\pi}{4} + \frac{\sqrt{\pi^{2} + 16 + 24 \pi}}{4}\right)\right)$$
=
-4 + pi
$$-4 + \pi$$
producto
            /             __________________\ /        __________________     \
            |            /        2         | |       /        2              |
  /     pi\ |     pi   \/  16 + pi  + 24*pi | |     \/  16 + pi  + 24*pi    pi|
0*|-2 + --|*|-1 + -- + ---------------------|*|-1 - --------------------- + --|
  \     2 / \     4              4          / \               4             4 /
$$0 \left(-2 + \frac{\pi}{2}\right) \left(-1 + \frac{\pi}{4} + \frac{\sqrt{\pi^{2} + 16 + 24 \pi}}{4}\right) \left(- \frac{\sqrt{\pi^{2} + 16 + 24 \pi}}{4} - 1 + \frac{\pi}{4}\right)$$
=
0
$$0$$
0
Respuesta rápida [src]
a1 = 0
$$a_{1} = 0$$
          pi
a2 = -2 + --
          2 
$$a_{2} = -2 + \frac{\pi}{2}$$
                  __________________
                 /        2         
          pi   \/  16 + pi  + 24*pi 
a3 = -1 + -- + ---------------------
          4              4          
$$a_{3} = -1 + \frac{\pi}{4} + \frac{\sqrt{\pi^{2} + 16 + 24 \pi}}{4}$$
             __________________     
            /        2              
          \/  16 + pi  + 24*pi    pi
a4 = -1 - --------------------- + --
                    4             4 
$$a_{4} = - \frac{\sqrt{\pi^{2} + 16 + 24 \pi}}{4} - 1 + \frac{\pi}{4}$$
a4 = -sqrt(pi^2 + 16 + 24*pi)/4 - 1 + pi/4
Respuesta numérica [src]
a1 = 58.0671627588811
a2 = -80.0703721429281
a3 = -55.0371053012787
a4 = -10.6316106205627
a5 = 58.1716745820683
a6 = 64.355304387026
a7 = 39.3458913582953
a8 = -48.6273094646995
a9 = -17.481682797262
a10 = -23.7066742426997
a11 = 26.812573032838
a12 = -67.4962760785148
a13 = -86.431006965611
a14 = 2.30119609953079
a15 = 347.136990055499
a16 = 51.8945702343708
a17 = 39.1936441558973
a18 = 32.8966973619698
a19 = -92.642324056455
a20 = -80.1508117710966
a21 = 51.7778608292377
a22 = 45.6190668960702
a23 = 26.5936673308499
a24 = -17.0702970378547
a25 = 83.2153388041046
a26 = 89.5696988394514
a27 = 76.9292173548358
a28 = -318.861739628117
a29 = -42.4890919104773
a30 = -92.711616030166
a31 = 20.2793430341583
a32 = 102.07157439505
a33 = -98.9925586260164
a34 = 95.7864488587
a35 = -11.3322138775699
a36 = -29.7318455505735
a37 = 7.52412534374267
a38 = -61.2079964686707
a39 = -73.8711388227521
a40 = -67.5921379243537
a41 = -61.3140221743956
a42 = 8.16309921581422
a43 = -42.3336106320223
a44 = 45.4869364897663
a45 = 70.6425874487008
a46 = -36.2201209385729
a47 = 83.2890399785379
a48 = 13.940079298441
a49 = -48.7618689170946
a50 = 14.3295538660729
a51 = 20.5596096513712
a52 = -940.903653727746
a53 = 33.0762874341853
a54 = -36.0360135005504
a55 = -5.58797766712013
a56 = -98.927756895554
a57 = -54.9185048199572
a58 = -23.4152460197019
a59 = -86.356556142174
a60 = 89.5010566778701
a61 = -29.9575005067565
a62 = 70.7290305607043
a63 = 64.4499269923487
a64 = 95.8506819207927
a65 = -73.7836626287997
a66 = 77.00878258808
a66 = 77.00878258808