Sr Examen
Otras calculadoras
- Sistemas de desigualdades paso a paso
- Ecuaciones básicas paso a paso
- Sistemas de ecuaciones paso a paso
- Solución de desigualdades trigonométricas en línea
- Resolución de desigualdades exponenciales en línea
- Resolución de desigualdades con un módulo en línea
-
¿Cómo usar?
- Desigualdades:
-
(x+1)*(x-9)>0
-
x^2+x-6>0
-
(x-1)/(x-4)>0
-
-16/(x+2)^2-5>=0
-
Expresiones idénticas
- abs(sin(tres *x-pi/ diez))<= uno
- abs( seno de (3 multiplicar por x menos número pi dividir por 10)) menos o igual a 1
- abs( seno de (tres multiplicar por x menos número pi dividir por diez)) menos o igual a uno
- abs(sin(3x-pi/10))<=1
- abssin3x-pi/10<=1
- abs(sin(3*x-pi dividir por 10))<=1
-
Expresiones semejantes
- abs(sin(3*x+pi/10))<=1
-
Expresiones con funciones
- abs
- abs(x-3)*(abs(x-4)+abs(x+5)-abs(2x+1))<=0
- abs(1/(lg0,5/lg((3-x)^2)+2))*(x^2-16)<=0
- abs((2-x)/(3x+1))>1
- abs(2x+1)>1-2abs(x-1)
- abs(sin(3x))<=sqrt(2)/2
- Seno sin
- sin(x)>0
- sin(x)<sqrt(3)/2
- sin(x)<√3/2
- sinx>-1
- sin(x)>1/2
abs(sin(3*x-pi/10))<=1 desigualdades
Solución
Ha introducido
[src]
| / pi\| |sin|3*x - --|| <= 1 | \ 10/|
$$\left|{\sin{\left(3 x - \frac{\pi}{10} \right)}}\right| \leq 1$$
Abs(sin(3*x - pi/10)) <= 1
Solución detallada
Se da la desigualdad:
$$\left|{\sin{\left(3 x - \frac{\pi}{10} \right)}}\right| \leq 1$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left|{\sin{\left(3 x - \frac{\pi}{10} \right)}}\right| = 1$$
Resolvemos:
$$x_{1} = 20.5250718699302$$
$$x_{2} = 32.0442449843762$$
$$x_{3} = -40.2123858362703$$
$$x_{4} = 7.95870142886166$$
$$x_{5} = 64.5073690249283$$
$$x_{6} = -18.221237455399$$
$$x_{7} = -93.6194611538848$$
$$x_{8} = -32.8820030751484$$
$$x_{9} = -60.1091393549168$$
$$x_{10} = 62.4129739593116$$
$$x_{11} = -27.6460154151684$$
$$x_{12} = -42.3067809590173$$
$$x_{13} = -16.1268421953888$$
$$x_{14} = -45.4483738362224$$
$$x_{15} = -75.8171026423729$$
$$x_{16} = -69.5339175134809$$
$$x_{17} = 36.2330352846171$$
$$x_{18} = -73.7227076232662$$
$$x_{19} = -80.0058929046049$$
$$x_{20} = 42.5162204469202$$
$$x_{21} = 82.3097274849022$$
$$x_{22} = -89.4306709513943$$
$$x_{23} = 12.1474917222297$$
$$x_{24} = 10.0530963775473$$
$$x_{25} = -91.5250660919517$$
$$x_{26} = -82.1002879349516$$
$$x_{27} = -47.5427689349152$$
$$x_{28} = -80.0058934025483$$
$$x_{29} = 38.3274303245094$$
$$x_{30} = 49.8466035427145$$
$$x_{31} = -25.5516203562555$$
$$x_{32} = -71.6283125744132$$
$$x_{33} = 66.6017644647288$$
$$x_{34} = -20.3156324032292$$
$$x_{35} = 98.017690767631$$
$$x_{36} = 84.4041225384348$$
$$x_{37} = 19.4778744705771$$
$$x_{38} = -14.0324471535272$$
$$x_{39} = 34.1386403007538$$
$$x_{40} = -51.7315590422159$$
$$x_{41} = -18.2212372580244$$
$$x_{42} = 67.648961616304$$
$$x_{43} = -9.84365687314419$$
$$x_{44} = 73.9321470569754$$
$$x_{45} = 86.4985176030388$$
$$x_{46} = -95.7138562041151$$
$$x_{47} = 45.6578133459306$$
$$x_{48} = 88.5929128949465$$
$$x_{49} = 1.67551646514494$$
$$x_{50} = 95.9232957543617$$
$$x_{51} = 25.7610598981097$$
$$x_{52} = 23.6666646755538$$
$$x_{53} = 69.7433570537668$$
$$x_{54} = -97.808251228532$$
$$x_{55} = 58.2241838672143$$
$$x_{56} = -62.2035344146363$$
$$x_{57} = 5.86430638412844$$
$$x_{58} = 73.9321471734816$$
$$x_{59} = 71.8377521217967$$
$$x_{60} = 60.31857890464$$
$$x_{61} = 54.0353935832461$$
$$x_{62} = 91.7345056314154$$
$$x_{63} = 100.112086213825$$
$$x_{64} = -3.5604717775025$$
$$x_{65} = -29.7404104609384$$
$$x_{66} = -31.8348054652383$$
$$x_{67} = -53.8259540547656$$
$$x_{68} = -23.457225270397$$
$$x_{69} = 16.3362817445022$$
$$x_{70} = -5.65486683538852$$
$$x_{71} = -7.74926187940205$$
$$x_{72} = -84.1946829931234$$
$$x_{73} = 29.9498500107811$$
$$x_{74} = 93.8289007007452$$
$$x_{75} = 1.67551614398222$$
$$x_{76} = 47.752208475998$$
$$x_{77} = -11.9380522429008$$
$$x_{78} = -49.6371639948421$$
$$x_{79} = -38.117990775067$$
$$x_{80} = 80.2153324503071$$
$$x_{81} = -86.2890780839411$$
$$x_{82} = -36.0235957364784$$
$$x_{83} = 51.9409985923026$$
$$x_{84} = -64.2979295198584$$
$$x_{85} = -67.4395223973879$$
$$x_{86} = 3.7699113201022$$
$$x_{87} = 27.8554549634938$$
$$x_{88} = 14.2418867024331$$
$$x_{89} = -33.9292008878596$$
$$x_{90} = 40.4218253802812$$
$$x_{91} = 18.4306768013431$$
$$x_{92} = -1.46607670137652$$
$$x_{93} = 45.6578131767162$$
$$x_{94} = -58.0147443201153$$
$$x_{95} = 56.1297887027462$$
$$x_{96} = 76.0265421771106$$
$$x_{1} = 20.5250718699302$$
$$x_{2} = 32.0442449843762$$
$$x_{3} = -40.2123858362703$$
$$x_{4} = 7.95870142886166$$
$$x_{5} = 64.5073690249283$$
$$x_{6} = -18.221237455399$$
$$x_{7} = -93.6194611538848$$
$$x_{8} = -32.8820030751484$$
$$x_{9} = -60.1091393549168$$
$$x_{10} = 62.4129739593116$$
$$x_{11} = -27.6460154151684$$
$$x_{12} = -42.3067809590173$$
$$x_{13} = -16.1268421953888$$
$$x_{14} = -45.4483738362224$$
$$x_{15} = -75.8171026423729$$
$$x_{16} = -69.5339175134809$$
$$x_{17} = 36.2330352846171$$
$$x_{18} = -73.7227076232662$$
$$x_{19} = -80.0058929046049$$
$$x_{20} = 42.5162204469202$$
$$x_{21} = 82.3097274849022$$
$$x_{22} = -89.4306709513943$$
$$x_{23} = 12.1474917222297$$
$$x_{24} = 10.0530963775473$$
$$x_{25} = -91.5250660919517$$
$$x_{26} = -82.1002879349516$$
$$x_{27} = -47.5427689349152$$
$$x_{28} = -80.0058934025483$$
$$x_{29} = 38.3274303245094$$
$$x_{30} = 49.8466035427145$$
$$x_{31} = -25.5516203562555$$
$$x_{32} = -71.6283125744132$$
$$x_{33} = 66.6017644647288$$
$$x_{34} = -20.3156324032292$$
$$x_{35} = 98.017690767631$$
$$x_{36} = 84.4041225384348$$
$$x_{37} = 19.4778744705771$$
$$x_{38} = -14.0324471535272$$
$$x_{39} = 34.1386403007538$$
$$x_{40} = -51.7315590422159$$
$$x_{41} = -18.2212372580244$$
$$x_{42} = 67.648961616304$$
$$x_{43} = -9.84365687314419$$
$$x_{44} = 73.9321470569754$$
$$x_{45} = 86.4985176030388$$
$$x_{46} = -95.7138562041151$$
$$x_{47} = 45.6578133459306$$
$$x_{48} = 88.5929128949465$$
$$x_{49} = 1.67551646514494$$
$$x_{50} = 95.9232957543617$$
$$x_{51} = 25.7610598981097$$
$$x_{52} = 23.6666646755538$$
$$x_{53} = 69.7433570537668$$
$$x_{54} = -97.808251228532$$
$$x_{55} = 58.2241838672143$$
$$x_{56} = -62.2035344146363$$
$$x_{57} = 5.86430638412844$$
$$x_{58} = 73.9321471734816$$
$$x_{59} = 71.8377521217967$$
$$x_{60} = 60.31857890464$$
$$x_{61} = 54.0353935832461$$
$$x_{62} = 91.7345056314154$$
$$x_{63} = 100.112086213825$$
$$x_{64} = -3.5604717775025$$
$$x_{65} = -29.7404104609384$$
$$x_{66} = -31.8348054652383$$
$$x_{67} = -53.8259540547656$$
$$x_{68} = -23.457225270397$$
$$x_{69} = 16.3362817445022$$
$$x_{70} = -5.65486683538852$$
$$x_{71} = -7.74926187940205$$
$$x_{72} = -84.1946829931234$$
$$x_{73} = 29.9498500107811$$
$$x_{74} = 93.8289007007452$$
$$x_{75} = 1.67551614398222$$
$$x_{76} = 47.752208475998$$
$$x_{77} = -11.9380522429008$$
$$x_{78} = -49.6371639948421$$
$$x_{79} = -38.117990775067$$
$$x_{80} = 80.2153324503071$$
$$x_{81} = -86.2890780839411$$
$$x_{82} = -36.0235957364784$$
$$x_{83} = 51.9409985923026$$
$$x_{84} = -64.2979295198584$$
$$x_{85} = -67.4395223973879$$
$$x_{86} = 3.7699113201022$$
$$x_{87} = 27.8554549634938$$
$$x_{88} = 14.2418867024331$$
$$x_{89} = -33.9292008878596$$
$$x_{90} = 40.4218253802812$$
$$x_{91} = 18.4306768013431$$
$$x_{92} = -1.46607670137652$$
$$x_{93} = 45.6578131767162$$
$$x_{94} = -58.0147443201153$$
$$x_{95} = 56.1297887027462$$
$$x_{96} = 76.0265421771106$$
Las raíces dadas
$$x_{54} = -97.808251228532$$
$$x_{46} = -95.7138562041151$$
$$x_{7} = -93.6194611538848$$
$$x_{25} = -91.5250660919517$$
$$x_{22} = -89.4306709513943$$
$$x_{81} = -86.2890780839411$$
$$x_{72} = -84.1946829931234$$
$$x_{26} = -82.1002879349516$$
$$x_{28} = -80.0058934025483$$
$$x_{19} = -80.0058929046049$$
$$x_{15} = -75.8171026423729$$
$$x_{18} = -73.7227076232662$$
$$x_{32} = -71.6283125744132$$
$$x_{16} = -69.5339175134809$$
$$x_{85} = -67.4395223973879$$
$$x_{84} = -64.2979295198584$$
$$x_{56} = -62.2035344146363$$
$$x_{9} = -60.1091393549168$$
$$x_{94} = -58.0147443201153$$
$$x_{67} = -53.8259540547656$$
$$x_{40} = -51.7315590422159$$
$$x_{78} = -49.6371639948421$$
$$x_{27} = -47.5427689349152$$
$$x_{14} = -45.4483738362224$$
$$x_{12} = -42.3067809590173$$
$$x_{3} = -40.2123858362703$$
$$x_{79} = -38.117990775067$$
$$x_{82} = -36.0235957364784$$
$$x_{89} = -33.9292008878596$$
$$x_{8} = -32.8820030751484$$
$$x_{66} = -31.8348054652383$$
$$x_{65} = -29.7404104609384$$
$$x_{11} = -27.6460154151684$$
$$x_{31} = -25.5516203562555$$
$$x_{68} = -23.457225270397$$
$$x_{34} = -20.3156324032292$$
$$x_{6} = -18.221237455399$$
$$x_{41} = -18.2212372580244$$
$$x_{13} = -16.1268421953888$$
$$x_{38} = -14.0324471535272$$
$$x_{77} = -11.9380522429008$$
$$x_{43} = -9.84365687314419$$
$$x_{71} = -7.74926187940205$$
$$x_{70} = -5.65486683538852$$
$$x_{64} = -3.5604717775025$$
$$x_{92} = -1.46607670137652$$
$$x_{75} = 1.67551614398222$$
$$x_{49} = 1.67551646514494$$
$$x_{86} = 3.7699113201022$$
$$x_{57} = 5.86430638412844$$
$$x_{4} = 7.95870142886166$$
$$x_{24} = 10.0530963775473$$
$$x_{23} = 12.1474917222297$$
$$x_{88} = 14.2418867024331$$
$$x_{69} = 16.3362817445022$$
$$x_{91} = 18.4306768013431$$
$$x_{37} = 19.4778744705771$$
$$x_{1} = 20.5250718699302$$
$$x_{52} = 23.6666646755538$$
$$x_{51} = 25.7610598981097$$
$$x_{87} = 27.8554549634938$$
$$x_{73} = 29.9498500107811$$
$$x_{2} = 32.0442449843762$$
$$x_{39} = 34.1386403007538$$
$$x_{17} = 36.2330352846171$$
$$x_{29} = 38.3274303245094$$
$$x_{90} = 40.4218253802812$$
$$x_{20} = 42.5162204469202$$
$$x_{93} = 45.6578131767162$$
$$x_{47} = 45.6578133459306$$
$$x_{76} = 47.752208475998$$
$$x_{30} = 49.8466035427145$$
$$x_{83} = 51.9409985923026$$
$$x_{61} = 54.0353935832461$$
$$x_{95} = 56.1297887027462$$
$$x_{55} = 58.2241838672143$$
$$x_{60} = 60.31857890464$$
$$x_{10} = 62.4129739593116$$
$$x_{5} = 64.5073690249283$$
$$x_{33} = 66.6017644647288$$
$$x_{42} = 67.648961616304$$
$$x_{53} = 69.7433570537668$$
$$x_{59} = 71.8377521217967$$
$$x_{44} = 73.9321470569754$$
$$x_{58} = 73.9321471734816$$
$$x_{96} = 76.0265421771106$$
$$x_{80} = 80.2153324503071$$
$$x_{21} = 82.3097274849022$$
$$x_{36} = 84.4041225384348$$
$$x_{45} = 86.4985176030388$$
$$x_{48} = 88.5929128949465$$
$$x_{62} = 91.7345056314154$$
$$x_{74} = 93.8289007007452$$
$$x_{50} = 95.9232957543617$$
$$x_{35} = 98.017690767631$$
$$x_{63} = 100.112086213825$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{54}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{54} - \frac{1}{10}$$
=
$$-97.808251228532 + - \frac{1}{10}$$
=
$$-97.908251228532$$
lo sustituimos en la expresión
$$\left|{\sin{\left(3 x - \frac{\pi}{10} \right)}}\right| \leq 1$$
$$\left|{\sin{\left(\left(-97.908251228532\right) 3 - \frac{\pi}{10} \right)}}\right| \leq 1$$
significa que una de las soluciones de nuestra ecuación será con:
$$x \leq -97.808251228532$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \leq -97.808251228532$$
$$x \geq -95.7138562041151 \wedge x \leq -93.6194611538848$$
$$x \geq -91.5250660919517 \wedge x \leq -89.4306709513943$$
$$x \geq -86.2890780839411 \wedge x \leq -84.1946829931234$$
$$x \geq -82.1002879349516 \wedge x \leq -80.0058934025483$$
$$x \geq -80.0058929046049 \wedge x \leq -75.8171026423729$$
$$x \geq -73.7227076232662 \wedge x \leq -71.6283125744132$$
$$x \geq -69.5339175134809 \wedge x \leq -67.4395223973879$$
$$x \geq -64.2979295198584 \wedge x \leq -62.2035344146363$$
$$x \geq -60.1091393549168 \wedge x \leq -58.0147443201153$$
$$x \geq -53.8259540547656 \wedge x \leq -51.7315590422159$$
$$x \geq -49.6371639948421 \wedge x \leq -47.5427689349152$$
$$x \geq -45.4483738362224 \wedge x \leq -42.3067809590173$$
$$x \geq -40.2123858362703 \wedge x \leq -38.117990775067$$
$$x \geq -36.0235957364784 \wedge x \leq -33.9292008878596$$
$$x \geq -32.8820030751484 \wedge x \leq -31.8348054652383$$
$$x \geq -29.7404104609384 \wedge x \leq -27.6460154151684$$
$$x \geq -25.5516203562555 \wedge x \leq -23.457225270397$$
$$x \geq -20.3156324032292 \wedge x \leq -18.221237455399$$
$$x \geq -18.2212372580244 \wedge x \leq -16.1268421953888$$
$$x \geq -14.0324471535272 \wedge x \leq -11.9380522429008$$
$$x \geq -9.84365687314419 \wedge x \leq -7.74926187940205$$
$$x \geq -5.65486683538852 \wedge x \leq -3.5604717775025$$
$$x \geq -1.46607670137652 \wedge x \leq 1.67551614398222$$
$$x \geq 1.67551646514494 \wedge x \leq 3.7699113201022$$
$$x \geq 5.86430638412844 \wedge x \leq 7.95870142886166$$
$$x \geq 10.0530963775473 \wedge x \leq 12.1474917222297$$
$$x \geq 14.2418867024331 \wedge x \leq 16.3362817445022$$
$$x \geq 18.4306768013431 \wedge x \leq 19.4778744705771$$
$$x \geq 20.5250718699302 \wedge x \leq 23.6666646755538$$
$$x \geq 25.7610598981097 \wedge x \leq 27.8554549634938$$
$$x \geq 29.9498500107811 \wedge x \leq 32.0442449843762$$
$$x \geq 34.1386403007538 \wedge x \leq 36.2330352846171$$
$$x \geq 38.3274303245094 \wedge x \leq 40.4218253802812$$
$$x \geq 42.5162204469202 \wedge x \leq 45.6578131767162$$
$$x \geq 45.6578133459306 \wedge x \leq 47.752208475998$$
$$x \geq 49.8466035427145 \wedge x \leq 51.9409985923026$$
$$x \geq 54.0353935832461 \wedge x \leq 56.1297887027462$$
$$x \geq 58.2241838672143 \wedge x \leq 60.31857890464$$
$$x \geq 62.4129739593116 \wedge x \leq 64.5073690249283$$
$$x \geq 66.6017644647288 \wedge x \leq 67.648961616304$$
$$x \geq 69.7433570537668 \wedge x \leq 71.8377521217967$$
$$x \geq 73.9321470569754 \wedge x \leq 73.9321471734816$$
$$x \geq 76.0265421771106 \wedge x \leq 80.2153324503071$$
$$x \geq 82.3097274849022 \wedge x \leq 84.4041225384348$$
$$x \geq 86.4985176030388 \wedge x \leq 88.5929128949465$$
$$x \geq 91.7345056314154 \wedge x \leq 93.8289007007452$$
$$x \geq 95.9232957543617 \wedge x \leq 98.017690767631$$
$$x \geq 100.112086213825$$
$$\left|{\sin{\left(3 x - \frac{\pi}{10} \right)}}\right| \leq 1$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left|{\sin{\left(3 x - \frac{\pi}{10} \right)}}\right| = 1$$
Resolvemos:
$$x_{1} = 20.5250718699302$$
$$x_{2} = 32.0442449843762$$
$$x_{3} = -40.2123858362703$$
$$x_{4} = 7.95870142886166$$
$$x_{5} = 64.5073690249283$$
$$x_{6} = -18.221237455399$$
$$x_{7} = -93.6194611538848$$
$$x_{8} = -32.8820030751484$$
$$x_{9} = -60.1091393549168$$
$$x_{10} = 62.4129739593116$$
$$x_{11} = -27.6460154151684$$
$$x_{12} = -42.3067809590173$$
$$x_{13} = -16.1268421953888$$
$$x_{14} = -45.4483738362224$$
$$x_{15} = -75.8171026423729$$
$$x_{16} = -69.5339175134809$$
$$x_{17} = 36.2330352846171$$
$$x_{18} = -73.7227076232662$$
$$x_{19} = -80.0058929046049$$
$$x_{20} = 42.5162204469202$$
$$x_{21} = 82.3097274849022$$
$$x_{22} = -89.4306709513943$$
$$x_{23} = 12.1474917222297$$
$$x_{24} = 10.0530963775473$$
$$x_{25} = -91.5250660919517$$
$$x_{26} = -82.1002879349516$$
$$x_{27} = -47.5427689349152$$
$$x_{28} = -80.0058934025483$$
$$x_{29} = 38.3274303245094$$
$$x_{30} = 49.8466035427145$$
$$x_{31} = -25.5516203562555$$
$$x_{32} = -71.6283125744132$$
$$x_{33} = 66.6017644647288$$
$$x_{34} = -20.3156324032292$$
$$x_{35} = 98.017690767631$$
$$x_{36} = 84.4041225384348$$
$$x_{37} = 19.4778744705771$$
$$x_{38} = -14.0324471535272$$
$$x_{39} = 34.1386403007538$$
$$x_{40} = -51.7315590422159$$
$$x_{41} = -18.2212372580244$$
$$x_{42} = 67.648961616304$$
$$x_{43} = -9.84365687314419$$
$$x_{44} = 73.9321470569754$$
$$x_{45} = 86.4985176030388$$
$$x_{46} = -95.7138562041151$$
$$x_{47} = 45.6578133459306$$
$$x_{48} = 88.5929128949465$$
$$x_{49} = 1.67551646514494$$
$$x_{50} = 95.9232957543617$$
$$x_{51} = 25.7610598981097$$
$$x_{52} = 23.6666646755538$$
$$x_{53} = 69.7433570537668$$
$$x_{54} = -97.808251228532$$
$$x_{55} = 58.2241838672143$$
$$x_{56} = -62.2035344146363$$
$$x_{57} = 5.86430638412844$$
$$x_{58} = 73.9321471734816$$
$$x_{59} = 71.8377521217967$$
$$x_{60} = 60.31857890464$$
$$x_{61} = 54.0353935832461$$
$$x_{62} = 91.7345056314154$$
$$x_{63} = 100.112086213825$$
$$x_{64} = -3.5604717775025$$
$$x_{65} = -29.7404104609384$$
$$x_{66} = -31.8348054652383$$
$$x_{67} = -53.8259540547656$$
$$x_{68} = -23.457225270397$$
$$x_{69} = 16.3362817445022$$
$$x_{70} = -5.65486683538852$$
$$x_{71} = -7.74926187940205$$
$$x_{72} = -84.1946829931234$$
$$x_{73} = 29.9498500107811$$
$$x_{74} = 93.8289007007452$$
$$x_{75} = 1.67551614398222$$
$$x_{76} = 47.752208475998$$
$$x_{77} = -11.9380522429008$$
$$x_{78} = -49.6371639948421$$
$$x_{79} = -38.117990775067$$
$$x_{80} = 80.2153324503071$$
$$x_{81} = -86.2890780839411$$
$$x_{82} = -36.0235957364784$$
$$x_{83} = 51.9409985923026$$
$$x_{84} = -64.2979295198584$$
$$x_{85} = -67.4395223973879$$
$$x_{86} = 3.7699113201022$$
$$x_{87} = 27.8554549634938$$
$$x_{88} = 14.2418867024331$$
$$x_{89} = -33.9292008878596$$
$$x_{90} = 40.4218253802812$$
$$x_{91} = 18.4306768013431$$
$$x_{92} = -1.46607670137652$$
$$x_{93} = 45.6578131767162$$
$$x_{94} = -58.0147443201153$$
$$x_{95} = 56.1297887027462$$
$$x_{96} = 76.0265421771106$$
$$x_{1} = 20.5250718699302$$
$$x_{2} = 32.0442449843762$$
$$x_{3} = -40.2123858362703$$
$$x_{4} = 7.95870142886166$$
$$x_{5} = 64.5073690249283$$
$$x_{6} = -18.221237455399$$
$$x_{7} = -93.6194611538848$$
$$x_{8} = -32.8820030751484$$
$$x_{9} = -60.1091393549168$$
$$x_{10} = 62.4129739593116$$
$$x_{11} = -27.6460154151684$$
$$x_{12} = -42.3067809590173$$
$$x_{13} = -16.1268421953888$$
$$x_{14} = -45.4483738362224$$
$$x_{15} = -75.8171026423729$$
$$x_{16} = -69.5339175134809$$
$$x_{17} = 36.2330352846171$$
$$x_{18} = -73.7227076232662$$
$$x_{19} = -80.0058929046049$$
$$x_{20} = 42.5162204469202$$
$$x_{21} = 82.3097274849022$$
$$x_{22} = -89.4306709513943$$
$$x_{23} = 12.1474917222297$$
$$x_{24} = 10.0530963775473$$
$$x_{25} = -91.5250660919517$$
$$x_{26} = -82.1002879349516$$
$$x_{27} = -47.5427689349152$$
$$x_{28} = -80.0058934025483$$
$$x_{29} = 38.3274303245094$$
$$x_{30} = 49.8466035427145$$
$$x_{31} = -25.5516203562555$$
$$x_{32} = -71.6283125744132$$
$$x_{33} = 66.6017644647288$$
$$x_{34} = -20.3156324032292$$
$$x_{35} = 98.017690767631$$
$$x_{36} = 84.4041225384348$$
$$x_{37} = 19.4778744705771$$
$$x_{38} = -14.0324471535272$$
$$x_{39} = 34.1386403007538$$
$$x_{40} = -51.7315590422159$$
$$x_{41} = -18.2212372580244$$
$$x_{42} = 67.648961616304$$
$$x_{43} = -9.84365687314419$$
$$x_{44} = 73.9321470569754$$
$$x_{45} = 86.4985176030388$$
$$x_{46} = -95.7138562041151$$
$$x_{47} = 45.6578133459306$$
$$x_{48} = 88.5929128949465$$
$$x_{49} = 1.67551646514494$$
$$x_{50} = 95.9232957543617$$
$$x_{51} = 25.7610598981097$$
$$x_{52} = 23.6666646755538$$
$$x_{53} = 69.7433570537668$$
$$x_{54} = -97.808251228532$$
$$x_{55} = 58.2241838672143$$
$$x_{56} = -62.2035344146363$$
$$x_{57} = 5.86430638412844$$
$$x_{58} = 73.9321471734816$$
$$x_{59} = 71.8377521217967$$
$$x_{60} = 60.31857890464$$
$$x_{61} = 54.0353935832461$$
$$x_{62} = 91.7345056314154$$
$$x_{63} = 100.112086213825$$
$$x_{64} = -3.5604717775025$$
$$x_{65} = -29.7404104609384$$
$$x_{66} = -31.8348054652383$$
$$x_{67} = -53.8259540547656$$
$$x_{68} = -23.457225270397$$
$$x_{69} = 16.3362817445022$$
$$x_{70} = -5.65486683538852$$
$$x_{71} = -7.74926187940205$$
$$x_{72} = -84.1946829931234$$
$$x_{73} = 29.9498500107811$$
$$x_{74} = 93.8289007007452$$
$$x_{75} = 1.67551614398222$$
$$x_{76} = 47.752208475998$$
$$x_{77} = -11.9380522429008$$
$$x_{78} = -49.6371639948421$$
$$x_{79} = -38.117990775067$$
$$x_{80} = 80.2153324503071$$
$$x_{81} = -86.2890780839411$$
$$x_{82} = -36.0235957364784$$
$$x_{83} = 51.9409985923026$$
$$x_{84} = -64.2979295198584$$
$$x_{85} = -67.4395223973879$$
$$x_{86} = 3.7699113201022$$
$$x_{87} = 27.8554549634938$$
$$x_{88} = 14.2418867024331$$
$$x_{89} = -33.9292008878596$$
$$x_{90} = 40.4218253802812$$
$$x_{91} = 18.4306768013431$$
$$x_{92} = -1.46607670137652$$
$$x_{93} = 45.6578131767162$$
$$x_{94} = -58.0147443201153$$
$$x_{95} = 56.1297887027462$$
$$x_{96} = 76.0265421771106$$
Las raíces dadas
$$x_{54} = -97.808251228532$$
$$x_{46} = -95.7138562041151$$
$$x_{7} = -93.6194611538848$$
$$x_{25} = -91.5250660919517$$
$$x_{22} = -89.4306709513943$$
$$x_{81} = -86.2890780839411$$
$$x_{72} = -84.1946829931234$$
$$x_{26} = -82.1002879349516$$
$$x_{28} = -80.0058934025483$$
$$x_{19} = -80.0058929046049$$
$$x_{15} = -75.8171026423729$$
$$x_{18} = -73.7227076232662$$
$$x_{32} = -71.6283125744132$$
$$x_{16} = -69.5339175134809$$
$$x_{85} = -67.4395223973879$$
$$x_{84} = -64.2979295198584$$
$$x_{56} = -62.2035344146363$$
$$x_{9} = -60.1091393549168$$
$$x_{94} = -58.0147443201153$$
$$x_{67} = -53.8259540547656$$
$$x_{40} = -51.7315590422159$$
$$x_{78} = -49.6371639948421$$
$$x_{27} = -47.5427689349152$$
$$x_{14} = -45.4483738362224$$
$$x_{12} = -42.3067809590173$$
$$x_{3} = -40.2123858362703$$
$$x_{79} = -38.117990775067$$
$$x_{82} = -36.0235957364784$$
$$x_{89} = -33.9292008878596$$
$$x_{8} = -32.8820030751484$$
$$x_{66} = -31.8348054652383$$
$$x_{65} = -29.7404104609384$$
$$x_{11} = -27.6460154151684$$
$$x_{31} = -25.5516203562555$$
$$x_{68} = -23.457225270397$$
$$x_{34} = -20.3156324032292$$
$$x_{6} = -18.221237455399$$
$$x_{41} = -18.2212372580244$$
$$x_{13} = -16.1268421953888$$
$$x_{38} = -14.0324471535272$$
$$x_{77} = -11.9380522429008$$
$$x_{43} = -9.84365687314419$$
$$x_{71} = -7.74926187940205$$
$$x_{70} = -5.65486683538852$$
$$x_{64} = -3.5604717775025$$
$$x_{92} = -1.46607670137652$$
$$x_{75} = 1.67551614398222$$
$$x_{49} = 1.67551646514494$$
$$x_{86} = 3.7699113201022$$
$$x_{57} = 5.86430638412844$$
$$x_{4} = 7.95870142886166$$
$$x_{24} = 10.0530963775473$$
$$x_{23} = 12.1474917222297$$
$$x_{88} = 14.2418867024331$$
$$x_{69} = 16.3362817445022$$
$$x_{91} = 18.4306768013431$$
$$x_{37} = 19.4778744705771$$
$$x_{1} = 20.5250718699302$$
$$x_{52} = 23.6666646755538$$
$$x_{51} = 25.7610598981097$$
$$x_{87} = 27.8554549634938$$
$$x_{73} = 29.9498500107811$$
$$x_{2} = 32.0442449843762$$
$$x_{39} = 34.1386403007538$$
$$x_{17} = 36.2330352846171$$
$$x_{29} = 38.3274303245094$$
$$x_{90} = 40.4218253802812$$
$$x_{20} = 42.5162204469202$$
$$x_{93} = 45.6578131767162$$
$$x_{47} = 45.6578133459306$$
$$x_{76} = 47.752208475998$$
$$x_{30} = 49.8466035427145$$
$$x_{83} = 51.9409985923026$$
$$x_{61} = 54.0353935832461$$
$$x_{95} = 56.1297887027462$$
$$x_{55} = 58.2241838672143$$
$$x_{60} = 60.31857890464$$
$$x_{10} = 62.4129739593116$$
$$x_{5} = 64.5073690249283$$
$$x_{33} = 66.6017644647288$$
$$x_{42} = 67.648961616304$$
$$x_{53} = 69.7433570537668$$
$$x_{59} = 71.8377521217967$$
$$x_{44} = 73.9321470569754$$
$$x_{58} = 73.9321471734816$$
$$x_{96} = 76.0265421771106$$
$$x_{80} = 80.2153324503071$$
$$x_{21} = 82.3097274849022$$
$$x_{36} = 84.4041225384348$$
$$x_{45} = 86.4985176030388$$
$$x_{48} = 88.5929128949465$$
$$x_{62} = 91.7345056314154$$
$$x_{74} = 93.8289007007452$$
$$x_{50} = 95.9232957543617$$
$$x_{35} = 98.017690767631$$
$$x_{63} = 100.112086213825$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{54}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{54} - \frac{1}{10}$$
=
$$-97.808251228532 + - \frac{1}{10}$$
=
$$-97.908251228532$$
lo sustituimos en la expresión
$$\left|{\sin{\left(3 x - \frac{\pi}{10} \right)}}\right| \leq 1$$
$$\left|{\sin{\left(\left(-97.908251228532\right) 3 - \frac{\pi}{10} \right)}}\right| \leq 1$$
/ pi\
-sin|293.724753685596 + --| <= 1
\ 10/ significa que una de las soluciones de nuestra ecuación será con:
$$x \leq -97.808251228532$$
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x54 x46 x7 x25 x22 x81 x72 x26 x28 x19 x15 x18 x32 x16 x85 x84 x56 x9 x94 x67 x40 x78 x27 x14 x12 x3 x79 x82 x89 x8 x66 x65 x11 x31 x68 x34 x6 x41 x13 x38 x77 x43 x71 x70 x64 x92 x75 x49 x86 x57 x4 x24 x23 x88 x69 x91 x37 x1 x52 x51 x87 x73 x2 x39 x17 x29 x90 x20 x93 x47 x76 x30 x83 x61 x95 x55 x60 x10 x5 x33 x42 x53 x59 x44 x58 x96 x80 x21 x36 x45 x48 x62 x74 x50 x35 x63Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \leq -97.808251228532$$
$$x \geq -95.7138562041151 \wedge x \leq -93.6194611538848$$
$$x \geq -91.5250660919517 \wedge x \leq -89.4306709513943$$
$$x \geq -86.2890780839411 \wedge x \leq -84.1946829931234$$
$$x \geq -82.1002879349516 \wedge x \leq -80.0058934025483$$
$$x \geq -80.0058929046049 \wedge x \leq -75.8171026423729$$
$$x \geq -73.7227076232662 \wedge x \leq -71.6283125744132$$
$$x \geq -69.5339175134809 \wedge x \leq -67.4395223973879$$
$$x \geq -64.2979295198584 \wedge x \leq -62.2035344146363$$
$$x \geq -60.1091393549168 \wedge x \leq -58.0147443201153$$
$$x \geq -53.8259540547656 \wedge x \leq -51.7315590422159$$
$$x \geq -49.6371639948421 \wedge x \leq -47.5427689349152$$
$$x \geq -45.4483738362224 \wedge x \leq -42.3067809590173$$
$$x \geq -40.2123858362703 \wedge x \leq -38.117990775067$$
$$x \geq -36.0235957364784 \wedge x \leq -33.9292008878596$$
$$x \geq -32.8820030751484 \wedge x \leq -31.8348054652383$$
$$x \geq -29.7404104609384 \wedge x \leq -27.6460154151684$$
$$x \geq -25.5516203562555 \wedge x \leq -23.457225270397$$
$$x \geq -20.3156324032292 \wedge x \leq -18.221237455399$$
$$x \geq -18.2212372580244 \wedge x \leq -16.1268421953888$$
$$x \geq -14.0324471535272 \wedge x \leq -11.9380522429008$$
$$x \geq -9.84365687314419 \wedge x \leq -7.74926187940205$$
$$x \geq -5.65486683538852 \wedge x \leq -3.5604717775025$$
$$x \geq -1.46607670137652 \wedge x \leq 1.67551614398222$$
$$x \geq 1.67551646514494 \wedge x \leq 3.7699113201022$$
$$x \geq 5.86430638412844 \wedge x \leq 7.95870142886166$$
$$x \geq 10.0530963775473 \wedge x \leq 12.1474917222297$$
$$x \geq 14.2418867024331 \wedge x \leq 16.3362817445022$$
$$x \geq 18.4306768013431 \wedge x \leq 19.4778744705771$$
$$x \geq 20.5250718699302 \wedge x \leq 23.6666646755538$$
$$x \geq 25.7610598981097 \wedge x \leq 27.8554549634938$$
$$x \geq 29.9498500107811 \wedge x \leq 32.0442449843762$$
$$x \geq 34.1386403007538 \wedge x \leq 36.2330352846171$$
$$x \geq 38.3274303245094 \wedge x \leq 40.4218253802812$$
$$x \geq 42.5162204469202 \wedge x \leq 45.6578131767162$$
$$x \geq 45.6578133459306 \wedge x \leq 47.752208475998$$
$$x \geq 49.8466035427145 \wedge x \leq 51.9409985923026$$
$$x \geq 54.0353935832461 \wedge x \leq 56.1297887027462$$
$$x \geq 58.2241838672143 \wedge x \leq 60.31857890464$$
$$x \geq 62.4129739593116 \wedge x \leq 64.5073690249283$$
$$x \geq 66.6017644647288 \wedge x \leq 67.648961616304$$
$$x \geq 69.7433570537668 \wedge x \leq 71.8377521217967$$
$$x \geq 73.9321470569754 \wedge x \leq 73.9321471734816$$
$$x \geq 76.0265421771106 \wedge x \leq 80.2153324503071$$
$$x \geq 82.3097274849022 \wedge x \leq 84.4041225384348$$
$$x \geq 86.4985176030388 \wedge x \leq 88.5929128949465$$
$$x \geq 91.7345056314154 \wedge x \leq 93.8289007007452$$
$$x \geq 95.9232957543617 \wedge x \leq 98.017690767631$$
$$x \geq 100.112086213825$$
Solución de la desigualdad en el gráfico