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+4)(x-8)>0
-
(x+4)*(x-8)>0
-
(x-1)^2*(x-4)<=0
-
x^2+x-30<0
- Derivada de:
-
cost
-
1/3
- Integral de d{x}:
- cost
- 1/3
- Límite de la función:
-
1/3
-
Expresiones idénticas
- cost< uno / tres
- coseno de t menos 1 dividir por 3
- coseno de t menos uno dividir por tres
- cost<1 dividir por 3
-
Expresiones semejantes
- cos(t)<-1/2
- cos(t)>=-sqrt(2)/2
- cos(t)<=-(sqrt(2)/2)
- (sin2t)-((sin(t)+cos(t))^2)/(tg(t)+ctg(t))
-
Expresiones con funciones
- cost
- cost≤1/2
- cost>-1\7
- cost<√2
- cost>=-sqrt(2)/2
- cost≤-√2/2
cost<1/3 desigualdades
Solución
Solución detallada
Se da la desigualdad:
$$\cos{\left(t \right)} < \frac{1}{3}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\cos{\left(t \right)} = \frac{1}{3}$$
Resolvemos:
Tenemos la ecuación
$$\cos{\left(t \right)} = \frac{1}{3}$$
cambiamos
$$\cos{\left(t \right)} - \frac{1}{3} = 0$$
$$\cos{\left(t \right)} - \frac{1}{3} = 0$$
Sustituimos
$$w = \cos{\left(t \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = \frac{1}{3}$$
Obtenemos la respuesta: w = 1/3
hacemos cambio inverso
$$\cos{\left(t \right)} = w$$
sustituimos w:
$$x_{1} = -55.3177083472755$$
$$x_{2} = -38.9300712604183$$
$$x_{3} = 93.016820190353$$
$$x_{4} = -32.6468859532387$$
$$x_{5} = 70.3459977963162$$
$$x_{6} = -99.3000054975326$$
$$x_{7} = -64.0628124891366$$
$$x_{8} = 82.9123684106754$$
$$x_{9} = -42.7513377329163$$
$$x_{10} = -67.8840789616347$$
$$x_{11} = 13.7973300316999$$
$$x_{12} = 7.51414472452036$$
$$x_{13} = 80.4504495759938$$
$$x_{14} = -45.2132565675979$$
$$x_{15} = -61.6008936544551$$
$$x_{16} = -30.1849671185572$$
$$x_{17} = 45.2132565675979$$
$$x_{18} = -1.23095941734077$$
$$x_{19} = 11.3354111970184$$
$$x_{20} = 89.195553717855$$
$$x_{21} = -7.51414472452036$$
$$x_{22} = 20.0805153388795$$
$$x_{23} = -36.4681524257367$$
$$x_{24} = -57.7796271819571$$
$$x_{25} = 86.7336348831734$$
$$x_{26} = 67.8840789616347$$
$$x_{27} = -11.3354111970184$$
$$x_{28} = 30.1849671185572$$
$$x_{29} = 42.7513377329163$$
$$x_{30} = -95.4787390250346$$
$$x_{31} = 57.7796271819571$$
$$x_{32} = -5.05222588983881$$
$$x_{33} = -20.0805153388795$$
$$x_{34} = 17.618596504198$$
$$x_{35} = 74.1672642688143$$
$$x_{36} = 95.4787390250346$$
$$x_{37} = 1.23095941734077$$
$$x_{38} = 55.3177083472755$$
$$x_{39} = 61.6008936544551$$
$$x_{40} = -80.4504495759938$$
$$x_{41} = 51.4964418747775$$
$$x_{42} = 23.9017818113776$$
$$x_{43} = -89.195553717855$$
$$x_{44} = 32.6468859532387$$
$$x_{45} = -23.9017818113776$$
$$x_{46} = 76.6291831034958$$
$$x_{47} = -325.494676555998$$
$$x_{48} = -86.7336348831734$$
$$x_{49} = -26.3637006460591$$
$$x_{50} = 38.9300712604183$$
$$x_{51} = -51.4964418747775$$
$$x_{52} = 26.3637006460591$$
$$x_{53} = -82.9123684106754$$
$$x_{54} = -70.3459977963162$$
$$x_{55} = -76.6291831034958$$
$$x_{56} = 36.4681524257367$$
$$x_{57} = 5.05222588983881$$
$$x_{58} = 99.3000054975326$$
$$x_{59} = 64.0628124891366$$
$$x_{60} = -101.761924332214$$
$$x_{61} = -17.618596504198$$
$$x_{62} = -49.0345230400959$$
$$x_{63} = -93.016820190353$$
$$x_{64} = 49.0345230400959$$
$$x_{65} = -74.1672642688143$$
$$x_{66} = -13.7973300316999$$
$$x_{1} = -55.3177083472755$$
$$x_{2} = -38.9300712604183$$
$$x_{3} = 93.016820190353$$
$$x_{4} = -32.6468859532387$$
$$x_{5} = 70.3459977963162$$
$$x_{6} = -99.3000054975326$$
$$x_{7} = -64.0628124891366$$
$$x_{8} = 82.9123684106754$$
$$x_{9} = -42.7513377329163$$
$$x_{10} = -67.8840789616347$$
$$x_{11} = 13.7973300316999$$
$$x_{12} = 7.51414472452036$$
$$x_{13} = 80.4504495759938$$
$$x_{14} = -45.2132565675979$$
$$x_{15} = -61.6008936544551$$
$$x_{16} = -30.1849671185572$$
$$x_{17} = 45.2132565675979$$
$$x_{18} = -1.23095941734077$$
$$x_{19} = 11.3354111970184$$
$$x_{20} = 89.195553717855$$
$$x_{21} = -7.51414472452036$$
$$x_{22} = 20.0805153388795$$
$$x_{23} = -36.4681524257367$$
$$x_{24} = -57.7796271819571$$
$$x_{25} = 86.7336348831734$$
$$x_{26} = 67.8840789616347$$
$$x_{27} = -11.3354111970184$$
$$x_{28} = 30.1849671185572$$
$$x_{29} = 42.7513377329163$$
$$x_{30} = -95.4787390250346$$
$$x_{31} = 57.7796271819571$$
$$x_{32} = -5.05222588983881$$
$$x_{33} = -20.0805153388795$$
$$x_{34} = 17.618596504198$$
$$x_{35} = 74.1672642688143$$
$$x_{36} = 95.4787390250346$$
$$x_{37} = 1.23095941734077$$
$$x_{38} = 55.3177083472755$$
$$x_{39} = 61.6008936544551$$
$$x_{40} = -80.4504495759938$$
$$x_{41} = 51.4964418747775$$
$$x_{42} = 23.9017818113776$$
$$x_{43} = -89.195553717855$$
$$x_{44} = 32.6468859532387$$
$$x_{45} = -23.9017818113776$$
$$x_{46} = 76.6291831034958$$
$$x_{47} = -325.494676555998$$
$$x_{48} = -86.7336348831734$$
$$x_{49} = -26.3637006460591$$
$$x_{50} = 38.9300712604183$$
$$x_{51} = -51.4964418747775$$
$$x_{52} = 26.3637006460591$$
$$x_{53} = -82.9123684106754$$
$$x_{54} = -70.3459977963162$$
$$x_{55} = -76.6291831034958$$
$$x_{56} = 36.4681524257367$$
$$x_{57} = 5.05222588983881$$
$$x_{58} = 99.3000054975326$$
$$x_{59} = 64.0628124891366$$
$$x_{60} = -101.761924332214$$
$$x_{61} = -17.618596504198$$
$$x_{62} = -49.0345230400959$$
$$x_{63} = -93.016820190353$$
$$x_{64} = 49.0345230400959$$
$$x_{65} = -74.1672642688143$$
$$x_{66} = -13.7973300316999$$
Las raíces dadas
$$x_{47} = -325.494676555998$$
$$x_{60} = -101.761924332214$$
$$x_{6} = -99.3000054975326$$
$$x_{30} = -95.4787390250346$$
$$x_{63} = -93.016820190353$$
$$x_{43} = -89.195553717855$$
$$x_{48} = -86.7336348831734$$
$$x_{53} = -82.9123684106754$$
$$x_{40} = -80.4504495759938$$
$$x_{55} = -76.6291831034958$$
$$x_{65} = -74.1672642688143$$
$$x_{54} = -70.3459977963162$$
$$x_{10} = -67.8840789616347$$
$$x_{7} = -64.0628124891366$$
$$x_{15} = -61.6008936544551$$
$$x_{24} = -57.7796271819571$$
$$x_{1} = -55.3177083472755$$
$$x_{51} = -51.4964418747775$$
$$x_{62} = -49.0345230400959$$
$$x_{14} = -45.2132565675979$$
$$x_{9} = -42.7513377329163$$
$$x_{2} = -38.9300712604183$$
$$x_{23} = -36.4681524257367$$
$$x_{4} = -32.6468859532387$$
$$x_{16} = -30.1849671185572$$
$$x_{49} = -26.3637006460591$$
$$x_{45} = -23.9017818113776$$
$$x_{33} = -20.0805153388795$$
$$x_{61} = -17.618596504198$$
$$x_{66} = -13.7973300316999$$
$$x_{27} = -11.3354111970184$$
$$x_{21} = -7.51414472452036$$
$$x_{32} = -5.05222588983881$$
$$x_{18} = -1.23095941734077$$
$$x_{37} = 1.23095941734077$$
$$x_{57} = 5.05222588983881$$
$$x_{12} = 7.51414472452036$$
$$x_{19} = 11.3354111970184$$
$$x_{11} = 13.7973300316999$$
$$x_{34} = 17.618596504198$$
$$x_{22} = 20.0805153388795$$
$$x_{42} = 23.9017818113776$$
$$x_{52} = 26.3637006460591$$
$$x_{28} = 30.1849671185572$$
$$x_{44} = 32.6468859532387$$
$$x_{56} = 36.4681524257367$$
$$x_{50} = 38.9300712604183$$
$$x_{29} = 42.7513377329163$$
$$x_{17} = 45.2132565675979$$
$$x_{64} = 49.0345230400959$$
$$x_{41} = 51.4964418747775$$
$$x_{38} = 55.3177083472755$$
$$x_{31} = 57.7796271819571$$
$$x_{39} = 61.6008936544551$$
$$x_{59} = 64.0628124891366$$
$$x_{26} = 67.8840789616347$$
$$x_{5} = 70.3459977963162$$
$$x_{35} = 74.1672642688143$$
$$x_{46} = 76.6291831034958$$
$$x_{13} = 80.4504495759938$$
$$x_{8} = 82.9123684106754$$
$$x_{25} = 86.7336348831734$$
$$x_{20} = 89.195553717855$$
$$x_{3} = 93.016820190353$$
$$x_{36} = 95.4787390250346$$
$$x_{58} = 99.3000054975326$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{47}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{47} - \frac{1}{10}$$
=
$$-325.494676555998 + - \frac{1}{10}$$
=
$$-325.594676555998$$
lo sustituimos en la expresión
$$\cos{\left(t \right)} < \frac{1}{3}$$
$$\cos{\left(t \right)} < \frac{1}{3}$$
Entonces
$$x < -325.494676555998$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -325.494676555998 \wedge x < -101.761924332214$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -325.494676555998 \wedge x < -101.761924332214$$
$$x > -99.3000054975326 \wedge x < -95.4787390250346$$
$$x > -93.016820190353 \wedge x < -89.195553717855$$
$$x > -86.7336348831734 \wedge x < -82.9123684106754$$
$$x > -80.4504495759938 \wedge x < -76.6291831034958$$
$$x > -74.1672642688143 \wedge x < -70.3459977963162$$
$$x > -67.8840789616347 \wedge x < -64.0628124891366$$
$$x > -61.6008936544551 \wedge x < -57.7796271819571$$
$$x > -55.3177083472755 \wedge x < -51.4964418747775$$
$$x > -49.0345230400959 \wedge x < -45.2132565675979$$
$$x > -42.7513377329163 \wedge x < -38.9300712604183$$
$$x > -36.4681524257367 \wedge x < -32.6468859532387$$
$$x > -30.1849671185572 \wedge x < -26.3637006460591$$
$$x > -23.9017818113776 \wedge x < -20.0805153388795$$
$$x > -17.618596504198 \wedge x < -13.7973300316999$$
$$x > -11.3354111970184 \wedge x < -7.51414472452036$$
$$x > -5.05222588983881 \wedge x < -1.23095941734077$$
$$x > 1.23095941734077 \wedge x < 5.05222588983881$$
$$x > 7.51414472452036 \wedge x < 11.3354111970184$$
$$x > 13.7973300316999 \wedge x < 17.618596504198$$
$$x > 20.0805153388795 \wedge x < 23.9017818113776$$
$$x > 26.3637006460591 \wedge x < 30.1849671185572$$
$$x > 32.6468859532387 \wedge x < 36.4681524257367$$
$$x > 38.9300712604183 \wedge x < 42.7513377329163$$
$$x > 45.2132565675979 \wedge x < 49.0345230400959$$
$$x > 51.4964418747775 \wedge x < 55.3177083472755$$
$$x > 57.7796271819571 \wedge x < 61.6008936544551$$
$$x > 64.0628124891366 \wedge x < 67.8840789616347$$
$$x > 70.3459977963162 \wedge x < 74.1672642688143$$
$$x > 76.6291831034958 \wedge x < 80.4504495759938$$
$$x > 82.9123684106754 \wedge x < 86.7336348831734$$
$$x > 89.195553717855 \wedge x < 93.016820190353$$
$$x > 95.4787390250346 \wedge x < 99.3000054975326$$
$$\cos{\left(t \right)} < \frac{1}{3}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\cos{\left(t \right)} = \frac{1}{3}$$
Resolvemos:
Tenemos la ecuación
$$\cos{\left(t \right)} = \frac{1}{3}$$
cambiamos
$$\cos{\left(t \right)} - \frac{1}{3} = 0$$
$$\cos{\left(t \right)} - \frac{1}{3} = 0$$
Sustituimos
$$w = \cos{\left(t \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = \frac{1}{3}$$
Obtenemos la respuesta: w = 1/3
hacemos cambio inverso
$$\cos{\left(t \right)} = w$$
sustituimos w:
$$x_{1} = -55.3177083472755$$
$$x_{2} = -38.9300712604183$$
$$x_{3} = 93.016820190353$$
$$x_{4} = -32.6468859532387$$
$$x_{5} = 70.3459977963162$$
$$x_{6} = -99.3000054975326$$
$$x_{7} = -64.0628124891366$$
$$x_{8} = 82.9123684106754$$
$$x_{9} = -42.7513377329163$$
$$x_{10} = -67.8840789616347$$
$$x_{11} = 13.7973300316999$$
$$x_{12} = 7.51414472452036$$
$$x_{13} = 80.4504495759938$$
$$x_{14} = -45.2132565675979$$
$$x_{15} = -61.6008936544551$$
$$x_{16} = -30.1849671185572$$
$$x_{17} = 45.2132565675979$$
$$x_{18} = -1.23095941734077$$
$$x_{19} = 11.3354111970184$$
$$x_{20} = 89.195553717855$$
$$x_{21} = -7.51414472452036$$
$$x_{22} = 20.0805153388795$$
$$x_{23} = -36.4681524257367$$
$$x_{24} = -57.7796271819571$$
$$x_{25} = 86.7336348831734$$
$$x_{26} = 67.8840789616347$$
$$x_{27} = -11.3354111970184$$
$$x_{28} = 30.1849671185572$$
$$x_{29} = 42.7513377329163$$
$$x_{30} = -95.4787390250346$$
$$x_{31} = 57.7796271819571$$
$$x_{32} = -5.05222588983881$$
$$x_{33} = -20.0805153388795$$
$$x_{34} = 17.618596504198$$
$$x_{35} = 74.1672642688143$$
$$x_{36} = 95.4787390250346$$
$$x_{37} = 1.23095941734077$$
$$x_{38} = 55.3177083472755$$
$$x_{39} = 61.6008936544551$$
$$x_{40} = -80.4504495759938$$
$$x_{41} = 51.4964418747775$$
$$x_{42} = 23.9017818113776$$
$$x_{43} = -89.195553717855$$
$$x_{44} = 32.6468859532387$$
$$x_{45} = -23.9017818113776$$
$$x_{46} = 76.6291831034958$$
$$x_{47} = -325.494676555998$$
$$x_{48} = -86.7336348831734$$
$$x_{49} = -26.3637006460591$$
$$x_{50} = 38.9300712604183$$
$$x_{51} = -51.4964418747775$$
$$x_{52} = 26.3637006460591$$
$$x_{53} = -82.9123684106754$$
$$x_{54} = -70.3459977963162$$
$$x_{55} = -76.6291831034958$$
$$x_{56} = 36.4681524257367$$
$$x_{57} = 5.05222588983881$$
$$x_{58} = 99.3000054975326$$
$$x_{59} = 64.0628124891366$$
$$x_{60} = -101.761924332214$$
$$x_{61} = -17.618596504198$$
$$x_{62} = -49.0345230400959$$
$$x_{63} = -93.016820190353$$
$$x_{64} = 49.0345230400959$$
$$x_{65} = -74.1672642688143$$
$$x_{66} = -13.7973300316999$$
$$x_{1} = -55.3177083472755$$
$$x_{2} = -38.9300712604183$$
$$x_{3} = 93.016820190353$$
$$x_{4} = -32.6468859532387$$
$$x_{5} = 70.3459977963162$$
$$x_{6} = -99.3000054975326$$
$$x_{7} = -64.0628124891366$$
$$x_{8} = 82.9123684106754$$
$$x_{9} = -42.7513377329163$$
$$x_{10} = -67.8840789616347$$
$$x_{11} = 13.7973300316999$$
$$x_{12} = 7.51414472452036$$
$$x_{13} = 80.4504495759938$$
$$x_{14} = -45.2132565675979$$
$$x_{15} = -61.6008936544551$$
$$x_{16} = -30.1849671185572$$
$$x_{17} = 45.2132565675979$$
$$x_{18} = -1.23095941734077$$
$$x_{19} = 11.3354111970184$$
$$x_{20} = 89.195553717855$$
$$x_{21} = -7.51414472452036$$
$$x_{22} = 20.0805153388795$$
$$x_{23} = -36.4681524257367$$
$$x_{24} = -57.7796271819571$$
$$x_{25} = 86.7336348831734$$
$$x_{26} = 67.8840789616347$$
$$x_{27} = -11.3354111970184$$
$$x_{28} = 30.1849671185572$$
$$x_{29} = 42.7513377329163$$
$$x_{30} = -95.4787390250346$$
$$x_{31} = 57.7796271819571$$
$$x_{32} = -5.05222588983881$$
$$x_{33} = -20.0805153388795$$
$$x_{34} = 17.618596504198$$
$$x_{35} = 74.1672642688143$$
$$x_{36} = 95.4787390250346$$
$$x_{37} = 1.23095941734077$$
$$x_{38} = 55.3177083472755$$
$$x_{39} = 61.6008936544551$$
$$x_{40} = -80.4504495759938$$
$$x_{41} = 51.4964418747775$$
$$x_{42} = 23.9017818113776$$
$$x_{43} = -89.195553717855$$
$$x_{44} = 32.6468859532387$$
$$x_{45} = -23.9017818113776$$
$$x_{46} = 76.6291831034958$$
$$x_{47} = -325.494676555998$$
$$x_{48} = -86.7336348831734$$
$$x_{49} = -26.3637006460591$$
$$x_{50} = 38.9300712604183$$
$$x_{51} = -51.4964418747775$$
$$x_{52} = 26.3637006460591$$
$$x_{53} = -82.9123684106754$$
$$x_{54} = -70.3459977963162$$
$$x_{55} = -76.6291831034958$$
$$x_{56} = 36.4681524257367$$
$$x_{57} = 5.05222588983881$$
$$x_{58} = 99.3000054975326$$
$$x_{59} = 64.0628124891366$$
$$x_{60} = -101.761924332214$$
$$x_{61} = -17.618596504198$$
$$x_{62} = -49.0345230400959$$
$$x_{63} = -93.016820190353$$
$$x_{64} = 49.0345230400959$$
$$x_{65} = -74.1672642688143$$
$$x_{66} = -13.7973300316999$$
Las raíces dadas
$$x_{47} = -325.494676555998$$
$$x_{60} = -101.761924332214$$
$$x_{6} = -99.3000054975326$$
$$x_{30} = -95.4787390250346$$
$$x_{63} = -93.016820190353$$
$$x_{43} = -89.195553717855$$
$$x_{48} = -86.7336348831734$$
$$x_{53} = -82.9123684106754$$
$$x_{40} = -80.4504495759938$$
$$x_{55} = -76.6291831034958$$
$$x_{65} = -74.1672642688143$$
$$x_{54} = -70.3459977963162$$
$$x_{10} = -67.8840789616347$$
$$x_{7} = -64.0628124891366$$
$$x_{15} = -61.6008936544551$$
$$x_{24} = -57.7796271819571$$
$$x_{1} = -55.3177083472755$$
$$x_{51} = -51.4964418747775$$
$$x_{62} = -49.0345230400959$$
$$x_{14} = -45.2132565675979$$
$$x_{9} = -42.7513377329163$$
$$x_{2} = -38.9300712604183$$
$$x_{23} = -36.4681524257367$$
$$x_{4} = -32.6468859532387$$
$$x_{16} = -30.1849671185572$$
$$x_{49} = -26.3637006460591$$
$$x_{45} = -23.9017818113776$$
$$x_{33} = -20.0805153388795$$
$$x_{61} = -17.618596504198$$
$$x_{66} = -13.7973300316999$$
$$x_{27} = -11.3354111970184$$
$$x_{21} = -7.51414472452036$$
$$x_{32} = -5.05222588983881$$
$$x_{18} = -1.23095941734077$$
$$x_{37} = 1.23095941734077$$
$$x_{57} = 5.05222588983881$$
$$x_{12} = 7.51414472452036$$
$$x_{19} = 11.3354111970184$$
$$x_{11} = 13.7973300316999$$
$$x_{34} = 17.618596504198$$
$$x_{22} = 20.0805153388795$$
$$x_{42} = 23.9017818113776$$
$$x_{52} = 26.3637006460591$$
$$x_{28} = 30.1849671185572$$
$$x_{44} = 32.6468859532387$$
$$x_{56} = 36.4681524257367$$
$$x_{50} = 38.9300712604183$$
$$x_{29} = 42.7513377329163$$
$$x_{17} = 45.2132565675979$$
$$x_{64} = 49.0345230400959$$
$$x_{41} = 51.4964418747775$$
$$x_{38} = 55.3177083472755$$
$$x_{31} = 57.7796271819571$$
$$x_{39} = 61.6008936544551$$
$$x_{59} = 64.0628124891366$$
$$x_{26} = 67.8840789616347$$
$$x_{5} = 70.3459977963162$$
$$x_{35} = 74.1672642688143$$
$$x_{46} = 76.6291831034958$$
$$x_{13} = 80.4504495759938$$
$$x_{8} = 82.9123684106754$$
$$x_{25} = 86.7336348831734$$
$$x_{20} = 89.195553717855$$
$$x_{3} = 93.016820190353$$
$$x_{36} = 95.4787390250346$$
$$x_{58} = 99.3000054975326$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{47}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{47} - \frac{1}{10}$$
=
$$-325.494676555998 + - \frac{1}{10}$$
=
$$-325.594676555998$$
lo sustituimos en la expresión
$$\cos{\left(t \right)} < \frac{1}{3}$$
$$\cos{\left(t \right)} < \frac{1}{3}$$
cos(t) < 1/3
Entonces
$$x < -325.494676555998$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -325.494676555998 \wedge x < -101.761924332214$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------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-------
x47 x60 x6 x30 x63 x43 x48 x53 x40 x55 x65 x54 x10 x7 x15 x24 x1 x51 x62 x14 x9 x2 x23 x4 x16 x49 x45 x33 x61 x66 x27 x21 x32 x18 x37 x57 x12 x19 x11 x34 x22 x42 x52 x28 x44 x56 x50 x29 x17 x64 x41 x38 x31 x39 x59 x26 x5 x35 x46 x13 x8 x25 x20 x3 x36 x58Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -325.494676555998 \wedge x < -101.761924332214$$
$$x > -99.3000054975326 \wedge x < -95.4787390250346$$
$$x > -93.016820190353 \wedge x < -89.195553717855$$
$$x > -86.7336348831734 \wedge x < -82.9123684106754$$
$$x > -80.4504495759938 \wedge x < -76.6291831034958$$
$$x > -74.1672642688143 \wedge x < -70.3459977963162$$
$$x > -67.8840789616347 \wedge x < -64.0628124891366$$
$$x > -61.6008936544551 \wedge x < -57.7796271819571$$
$$x > -55.3177083472755 \wedge x < -51.4964418747775$$
$$x > -49.0345230400959 \wedge x < -45.2132565675979$$
$$x > -42.7513377329163 \wedge x < -38.9300712604183$$
$$x > -36.4681524257367 \wedge x < -32.6468859532387$$
$$x > -30.1849671185572 \wedge x < -26.3637006460591$$
$$x > -23.9017818113776 \wedge x < -20.0805153388795$$
$$x > -17.618596504198 \wedge x < -13.7973300316999$$
$$x > -11.3354111970184 \wedge x < -7.51414472452036$$
$$x > -5.05222588983881 \wedge x < -1.23095941734077$$
$$x > 1.23095941734077 \wedge x < 5.05222588983881$$
$$x > 7.51414472452036 \wedge x < 11.3354111970184$$
$$x > 13.7973300316999 \wedge x < 17.618596504198$$
$$x > 20.0805153388795 \wedge x < 23.9017818113776$$
$$x > 26.3637006460591 \wedge x < 30.1849671185572$$
$$x > 32.6468859532387 \wedge x < 36.4681524257367$$
$$x > 38.9300712604183 \wedge x < 42.7513377329163$$
$$x > 45.2132565675979 \wedge x < 49.0345230400959$$
$$x > 51.4964418747775 \wedge x < 55.3177083472755$$
$$x > 57.7796271819571 \wedge x < 61.6008936544551$$
$$x > 64.0628124891366 \wedge x < 67.8840789616347$$
$$x > 70.3459977963162 \wedge x < 74.1672642688143$$
$$x > 76.6291831034958 \wedge x < 80.4504495759938$$
$$x > 82.9123684106754 \wedge x < 86.7336348831734$$
$$x > 89.195553717855 \wedge x < 93.016820190353$$
$$x > 95.4787390250346 \wedge x < 99.3000054975326$$
Respuesta rápida
[src]
/ / ___\ / ___\ \ And\t < - atan\2*\/ 2 / + 2*pi, atan\2*\/ 2 / < t/
$$t < - \operatorname{atan}{\left(2 \sqrt{2} \right)} + 2 \pi \wedge \operatorname{atan}{\left(2 \sqrt{2} \right)} < t$$
(atan(2*sqrt(2)) < t)∧(t < -atan(2*sqrt(2)) + 2*pi)
Respuesta rápida 2
[src]
/ ___\ / ___\ (atan\2*\/ 2 /, - atan\2*\/ 2 / + 2*pi)
$$x\ in\ \left(\operatorname{atan}{\left(2 \sqrt{2} \right)}, - \operatorname{atan}{\left(2 \sqrt{2} \right)} + 2 \pi\right)$$
x in Interval.open(atan(2*sqrt(2)), -atan(2*sqrt(2)) + 2*pi)