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Expresiones semejantes
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Expresiones con funciones
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2*sin(x)^2*cot(x)+sin(4*x-pi/2)+1=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 / pi\
2*sin (x)*cot(x) + sin|4*x - --| + 1 = 0
\ 2 /
$$\left(2 \sin^{2}{\left(x \right)} \cot{\left(x \right)} + \sin{\left(4 x - \frac{\pi}{2} \right)}\right) + 1 = 0$$
Respuesta rápida
[src]
-pi
x1 = ----
2
$$x_{1} = - \frac{\pi}{2}$$
-5*pi
x2 = -----
12
$$x_{2} = - \frac{5 \pi}{12}$$
-pi
x3 = ----
12
$$x_{3} = - \frac{\pi}{12}$$
pi
x4 = --
2
$$x_{4} = \frac{\pi}{2}$$
/ ___ ___\
| \/ 2 \/ 6 |
|- ----- - -----|
/log(2) / ___\\ | 4 4 |
x5 = pi + I*|------ - log\\/ 2 /| + atan|---------------|
\ 2 / | ___ ___|
| \/ 2 \/ 6 |
|- ----- + -----|
\ 4 4 /
$$x_{5} = \operatorname{atan}{\left(\frac{- \frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4}}{- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} \right)} + \pi + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)$$
/ ___ ___\
| \/ 6 \/ 2 |
|- ----- + -----|
/log(2) / ___\\ | 4 4 |
x6 = pi + I*|------ - log\\/ 2 /| + atan|---------------|
\ 2 / | ___ ___ |
| \/ 2 \/ 6 |
| ----- + ----- |
\ 4 4 /
$$x_{6} = \operatorname{atan}{\left(\frac{- \frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4}}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} \right)} + \pi + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)$$
x6 = atan((-sqrt(6)/4 + sqrt(2)/4)/(sqrt(2)/4 + sqrt(6)/4)) + pi + i*(-log(sqrt(2)) + log(2)/2)
Suma y producto de raíces
[src]
suma
/ ___ ___\ / ___ ___\
| \/ 2 \/ 6 | | \/ 6 \/ 2 |
|- ----- - -----| |- ----- + -----|
pi 5*pi pi pi /log(2) / ___\\ | 4 4 | /log(2) / ___\\ | 4 4 |
- -- - ---- - -- + -- + pi + I*|------ - log\\/ 2 /| + atan|---------------| + pi + I*|------ - log\\/ 2 /| + atan|---------------|
2 12 12 2 \ 2 / | ___ ___| \ 2 / | ___ ___ |
| \/ 2 \/ 6 | | \/ 2 \/ 6 |
|- ----- + -----| | ----- + ----- |
\ 4 4 / \ 4 4 /
$$\left(\left(\left(\left(- \frac{\pi}{2} - \frac{5 \pi}{12}\right) - \frac{\pi}{12}\right) + \frac{\pi}{2}\right) + \left(\operatorname{atan}{\left(\frac{- \frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4}}{- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} \right)} + \pi + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right)\right) + \left(\operatorname{atan}{\left(\frac{- \frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4}}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} \right)} + \pi + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right)$$
=
/ ___ ___\ / ___ ___\
| \/ 2 \/ 6 | | \/ 6 \/ 2 |
|- ----- - -----| |- ----- + -----|
3*pi /log(2) / ___\\ | 4 4 | | 4 4 |
---- + 2*I*|------ - log\\/ 2 /| + atan|---------------| + atan|---------------|
2 \ 2 / | ___ ___| | ___ ___ |
| \/ 2 \/ 6 | | \/ 2 \/ 6 |
|- ----- + -----| | ----- + ----- |
\ 4 4 / \ 4 4 /
$$\operatorname{atan}{\left(\frac{- \frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4}}{- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} \right)} + \operatorname{atan}{\left(\frac{- \frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4}}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} \right)} + \frac{3 \pi}{2} + 2 i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)$$
producto
/ / ___ ___\\ / / ___ ___\\
| | \/ 2 \/ 6 || | | \/ 6 \/ 2 ||
| |- ----- - -----|| | |- ----- + -----||
-pi -5*pi -pi pi | /log(2) / ___\\ | 4 4 || | /log(2) / ___\\ | 4 4 ||
----*-----*----*--*|pi + I*|------ - log\\/ 2 /| + atan|---------------||*|pi + I*|------ - log\\/ 2 /| + atan|---------------||
2 12 12 2 | \ 2 / | ___ ___|| | \ 2 / | ___ ___ ||
| | \/ 2 \/ 6 || | | \/ 2 \/ 6 ||
| |- ----- + -----|| | | ----- + ----- ||
\ \ 4 4 // \ \ 4 4 //
$$\frac{\pi}{2} \cdot - \frac{\pi}{12} \cdot - \frac{\pi}{2} \left(- \frac{5 \pi}{12}\right) \left(\operatorname{atan}{\left(\frac{- \frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4}}{- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} \right)} + \pi + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(\frac{- \frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4}}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} \right)} + \pi + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right)$$
=
6 -385*pi -------- 82944
$$- \frac{385 \pi^{6}}{82944}$$
-385*pi^6/82944
Respuesta numérica
[src]
x1 = -57.857664703612
x2 = 14.1371669411541
x3 = 48.6946861306418
x4 = -72.2566310325652
x5 = -79.8488132787406
x6 = -80.1106126665397
x7 = -7.85398163397448
x8 = -59.6902604182061
x9 = -97.6511716490827
x10 = -39.0081087820733
x11 = -6.28318530717959
x12 = 72.2566310325652
x13 = 37.6991118430775
x14 = 80.1106126665397
x15 = 94.2477796076938
x16 = 39.5317075576716
x17 = -14.1371669411541
x18 = 1.83259571459405
x19 = 7.85398163397448
x20 = -29.845130209103
x21 = 70.6858347057703
x22 = -87.9645943005142
x23 = 67.8060414399797
x24 = 59.6902604182061
x25 = 42.4115008234622
x26 = -100.792764302673
x27 = 45.8148928648512
x28 = 89.7971900151083
x29 = -67.5442420521806
x30 = -17.0169602069447
x31 = -76.9690200129499
x32 = 8.11578102177363
x33 = -64.1408500107916
x34 = 100.269165527074
x35 = -86.1319985859202
x36 = -45.553093477052
x37 = -21.9911485751286
x38 = -23.5619449019235
x39 = 58.1194640914112
x40 = -36.1283155162826
x41 = -13.8753675533549
x42 = -60.9992573572018
x43 = 87.9645943005142
x44 = -51.8362787842316
x45 = -73.8274273593601
x46 = 4.71238898038469
x47 = 64.4026493985908
x48 = -9.68657734856853
x49 = -82.9904059323304
x50 = -42.4115008234622
x51 = -95.8185759344887
x52 = 81.6814089933346
x53 = -43.9822971502571
x54 = -37.6991118430775
x55 = -65.9734457253857
x56 = 20.4203522483337
x57 = 78.2780169519457
x58 = -1.5707963267949
x59 = 92.6769832808989
x60 = 6.28318530717959
x61 = -75.6600230739542
x62 = 499.513231920777
x63 = 28.2743338823081
x64 = 74.0892267471593
x65 = 23.8237442897226
x66 = -94.2477796076938
x67 = 86.3937979737193
x68 = -31.6777259236971
x69 = 56.2868683768171
x70 = 43.9822971502571
x71 = -42.1497014356631
x72 = 17.540558982543
x73 = -35.8665161284835
x74 = 65.9734457253857
x75 = 34.2957198016886
x76 = -15.707963267949
x77 = -50.2654824574367
x78 = 52.0980781720307
x79 = 50.0036830696375
x80 = 36.1283155162826
x81 = 15.707963267949
x82 = 30.1069295969022
x83 = -4.45058959258554
x84 = 26.7035375555132
x85 = 73.8274273593601
x86 = 96.0803753222878
x87 = 21.9911485751286
x88 = -28.2743338823081
x89 = -89.5353906273091
x90 = 12.30457122656
x91 = -53.6688744988256
x92 = -20.1585528605345
x92 = -20.1585528605345