Se da la desigualdad:
sin(y)<−21Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
sin(y)=−21Resolvemos:
x1=68.329640215578x2=73.0420291959627x3=−65.1880475619882x4=−46.3384916404494x5=62.0464549083984x6=−63.6172512351933x7=98.174770424681x8=−90.3207887907066x9=−38.484510006475x10=−128.019900633784x11=74.6128255227576x12=66.7588438887831x13=−51.0508806208341x14=−96.6039740978861x15=−27.4889357189107x16=5.49778714378214x17=−52.621676947629x18=80.8960108299372x19=−0.785398163397448x20=18.0641577581413x21=−40.0553063332699x22=93.4623814442964x23=−13.3517687777566x24=41.6261026600648x25=22.776546738526x26=3.92699081698724x27=−215482.625507887x28=91.8915851175014x29=55.7632696012188x30=−2.35619449019234x31=16.4933614313464x32=−101.316363078271x33=−8.63937979737193x34=10.2101761241668x35=11.7809724509617x36=−57.3340659280137x37=49.4800842940392x38=−830.165858711103x39=−77.7544181763474x40=−44.7676953136546x41=54.1924732744239x42=−69.9004365423729x43=−58.9048622548086x44=−76.1836218495525x45=652.665873783279x46=−2865.91789823729x47=−25.9181393921158x48=36.9137136796801x49=−371.493331286993x50=30.6305283725005x51=85.6083998103219x52=−19.6349540849362x53=−14.9225651045515x54=99.7455667514759x55=35.3429173528852x56=−21.2057504117311x57=−84.037603483527x58=29.0597320457056x59=87.1791961371168x60=−71.4712328691678x61=−82.4668071567321x62=−704.502152567511x63=60.4756585816035x64=−88.7499924639117x65=−32.2013246992954x66=43.1968989868597x67=−95.0331777710912x68=79.3252145031423x69=−33.7721210260903x70=47.9092879672443x71=−7.06858347057703x72=24.3473430653209x1=68.329640215578x2=73.0420291959627x3=−65.1880475619882x4=−46.3384916404494x5=62.0464549083984x6=−63.6172512351933x7=98.174770424681x8=−90.3207887907066x9=−38.484510006475x10=−128.019900633784x11=74.6128255227576x12=66.7588438887831x13=−51.0508806208341x14=−96.6039740978861x15=−27.4889357189107x16=5.49778714378214x17=−52.621676947629x18=80.8960108299372x19=−0.785398163397448x20=18.0641577581413x21=−40.0553063332699x22=93.4623814442964x23=−13.3517687777566x24=41.6261026600648x25=22.776546738526x26=3.92699081698724x27=−215482.625507887x28=91.8915851175014x29=55.7632696012188x30=−2.35619449019234x31=16.4933614313464x32=−101.316363078271x33=−8.63937979737193x34=10.2101761241668x35=11.7809724509617x36=−57.3340659280137x37=49.4800842940392x38=−830.165858711103x39=−77.7544181763474x40=−44.7676953136546x41=54.1924732744239x42=−69.9004365423729x43=−58.9048622548086x44=−76.1836218495525x45=652.665873783279x46=−2865.91789823729x47=−25.9181393921158x48=36.9137136796801x49=−371.493331286993x50=30.6305283725005x51=85.6083998103219x52=−19.6349540849362x53=−14.9225651045515x54=99.7455667514759x55=35.3429173528852x56=−21.2057504117311x57=−84.037603483527x58=29.0597320457056x59=87.1791961371168x60=−71.4712328691678x61=−82.4668071567321x62=−704.502152567511x63=60.4756585816035x64=−88.7499924639117x65=−32.2013246992954x66=43.1968989868597x67=−95.0331777710912x68=79.3252145031423x69=−33.7721210260903x70=47.9092879672443x71=−7.06858347057703x72=24.3473430653209Las raíces dadas
x27=−215482.625507887x46=−2865.91789823729x38=−830.165858711103x62=−704.502152567511x49=−371.493331286993x10=−128.019900633784x32=−101.316363078271x14=−96.6039740978861x67=−95.0331777710912x8=−90.3207887907066x64=−88.7499924639117x57=−84.037603483527x61=−82.4668071567321x39=−77.7544181763474x44=−76.1836218495525x60=−71.4712328691678x42=−69.9004365423729x3=−65.1880475619882x6=−63.6172512351933x43=−58.9048622548086x36=−57.3340659280137x17=−52.621676947629x13=−51.0508806208341x4=−46.3384916404494x40=−44.7676953136546x21=−40.0553063332699x9=−38.484510006475x69=−33.7721210260903x65=−32.2013246992954x15=−27.4889357189107x47=−25.9181393921158x56=−21.2057504117311x52=−19.6349540849362x53=−14.9225651045515x23=−13.3517687777566x33=−8.63937979737193x71=−7.06858347057703x30=−2.35619449019234x19=−0.785398163397448x26=3.92699081698724x16=5.49778714378214x34=10.2101761241668x35=11.7809724509617x31=16.4933614313464x20=18.0641577581413x25=22.776546738526x72=24.3473430653209x58=29.0597320457056x50=30.6305283725005x55=35.3429173528852x48=36.9137136796801x24=41.6261026600648x66=43.1968989868597x70=47.9092879672443x37=49.4800842940392x41=54.1924732744239x29=55.7632696012188x63=60.4756585816035x5=62.0464549083984x12=66.7588438887831x1=68.329640215578x2=73.0420291959627x11=74.6128255227576x68=79.3252145031423x18=80.8960108299372x51=85.6083998103219x59=87.1791961371168x28=91.8915851175014x22=93.4623814442964x7=98.174770424681x54=99.7455667514759x45=652.665873783279son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
x0<x27Consideremos, por ejemplo, el punto
x0=x27−101=
−215482.625507887+−101=
−215482.725507887lo sustituimos en la expresión
sin(y)<−21sin(y)<−21 ___
-\/ 2
sin(y) < -------
2
Entonces
x<−215482.625507887no se cumple
significa que una de las soluciones de nuestra ecuación será con:
x>−215482.625507887∧x<−2865.91789823729 _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------
x27 x46 x38 x62 x49 x10 x32 x14 x67 x8 x64 x57 x61 x39 x44 x60 x42 x3 x6 x43 x36 x17 x13 x4 x40 x21 x9 x69 x65 x15 x47 x56 x52 x53 x23 x33 x71 x30 x19 x26 x16 x34 x35 x31 x20 x25 x72 x58 x50 x55 x48 x24 x66 x70 x37 x41 x29 x63 x5 x12 x1 x2 x11 x68 x18 x51 x59 x28 x22 x7 x54 x45Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
x>−215482.625507887∧x<−2865.91789823729x>−830.165858711103∧x<−704.502152567511x>−371.493331286993∧x<−128.019900633784x>−101.316363078271∧x<−96.6039740978861x>−95.0331777710912∧x<−90.3207887907066x>−88.7499924639117∧x<−84.037603483527x>−82.4668071567321∧x<−77.7544181763474x>−76.1836218495525∧x<−71.4712328691678x>−69.9004365423729∧x<−65.1880475619882x>−63.6172512351933∧x<−58.9048622548086x>−57.3340659280137∧x<−52.621676947629x>−51.0508806208341∧x<−46.3384916404494x>−44.7676953136546∧x<−40.0553063332699x>−38.484510006475∧x<−33.7721210260903x>−32.2013246992954∧x<−27.4889357189107x>−25.9181393921158∧x<−21.2057504117311x>−19.6349540849362∧x<−14.9225651045515x>−13.3517687777566∧x<−8.63937979737193x>−7.06858347057703∧x<−2.35619449019234x>−0.785398163397448∧x<3.92699081698724x>5.49778714378214∧x<10.2101761241668x>11.7809724509617∧x<16.4933614313464x>18.0641577581413∧x<22.776546738526x>24.3473430653209∧x<29.0597320457056x>30.6305283725005∧x<35.3429173528852x>36.9137136796801∧x<41.6261026600648x>43.1968989868597∧x<47.9092879672443x>49.4800842940392∧x<54.1924732744239x>55.7632696012188∧x<60.4756585816035x>62.0464549083984∧x<66.7588438887831x>68.329640215578∧x<73.0420291959627x>74.6128255227576∧x<79.3252145031423x>80.8960108299372∧x<85.6083998103219x>87.1791961371168∧x<91.8915851175014x>93.4623814442964∧x<98.174770424681x>99.7455667514759∧x<652.665873783279
-x^2-2x+3>0
x^2>9
x^2-10x<0
(x^2-x-1)*(x^2-x-7)<-5
sin(y)