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+8)(x-5)>0
-
(x+8)*(x-5)>0
- (x-7)^2<sqrt11(x-7)
-
(x^2-x-6)*sqrt(8-x)<=0
- Integral de d{x}:
- sin(t/2)
-
Expresiones idénticas
- sin(t/ dos)<= uno / dos
- seno de (t dividir por 2) menos o igual a 1 dividir por 2
- seno de (t dividir por dos) menos o igual a uno dividir por dos
- sint/2<=1/2
- sin(t dividir por 2)<=1 dividir por 2
-
Expresiones con funciones
- Seno sin
- sin(x)<=0
- sin(x)>0.5
- sin(t)>=1/2
- sin(pi/4-x/4)<1
- sin(x)>=-11/12
sin(t/2)<=1/2 desigualdades
Solución
Ha introducido
[src]
/t\ sin|-| <= 1/2 \2/
$$\sin{\left(\frac{t}{2} \right)} \leq \frac{1}{2}$$
sin(t/2) <= 1/2
Solución detallada
Se da la desigualdad:
$$\sin{\left(\frac{t}{2} \right)} \leq \frac{1}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\sin{\left(\frac{t}{2} \right)} = \frac{1}{2}$$
Resolvemos:
$$x_{1} = -24.0855436775217$$
$$x_{2} = -32.4631240870945$$
$$x_{3} = 26.1799387799149$$
$$x_{4} = -346.622389446074$$
$$x_{5} = -7.33038285837618$$
$$x_{6} = 17.8023583703422$$
$$x_{7} = -95.2949771588904$$
$$x_{8} = -86.9173967493176$$
$$x_{9} = 80.634211442138$$
$$x_{10} = -19.8967534727354$$
$$x_{11} = 114.144533080429$$
$$x_{12} = 38.7463093942741$$
$$x_{13} = 5.23598775598299$$
$$x_{14} = 59100.6881968824$$
$$x_{15} = -45.0294947014537$$
$$x_{16} = 1.0471975511966$$
$$x_{17} = -11.5191730631626$$
$$x_{18} = -74.3510261349584$$
$$x_{19} = -57.5958653158129$$
$$x_{20} = 42.9350995990605$$
$$x_{21} = 76.4454212373516$$
$$x_{22} = 55.5014702134197$$
$$x_{23} = 331.961623729322$$
$$x_{24} = 89.0117918517108$$
$$x_{25} = 68.0678408277789$$
$$x_{26} = 63.8790506229925$$
$$x_{27} = 101.57816246607$$
$$x_{28} = -99.4837673636768$$
$$x_{29} = 51.3126800086333$$
$$x_{30} = -49.2182849062401$$
$$x_{31} = -36.6519142918809$$
$$x_{32} = 105.766952670856$$
$$x_{33} = 13.6135681655558$$
$$x_{34} = -70.162235930172$$
$$x_{35} = 93.2005820564972$$
$$x_{36} = -82.7286065445312$$
$$x_{37} = -61.7846555205993$$
$$x_{38} = 30.3687289847013$$
$$x_{1} = -24.0855436775217$$
$$x_{2} = -32.4631240870945$$
$$x_{3} = 26.1799387799149$$
$$x_{4} = -346.622389446074$$
$$x_{5} = -7.33038285837618$$
$$x_{6} = 17.8023583703422$$
$$x_{7} = -95.2949771588904$$
$$x_{8} = -86.9173967493176$$
$$x_{9} = 80.634211442138$$
$$x_{10} = -19.8967534727354$$
$$x_{11} = 114.144533080429$$
$$x_{12} = 38.7463093942741$$
$$x_{13} = 5.23598775598299$$
$$x_{14} = 59100.6881968824$$
$$x_{15} = -45.0294947014537$$
$$x_{16} = 1.0471975511966$$
$$x_{17} = -11.5191730631626$$
$$x_{18} = -74.3510261349584$$
$$x_{19} = -57.5958653158129$$
$$x_{20} = 42.9350995990605$$
$$x_{21} = 76.4454212373516$$
$$x_{22} = 55.5014702134197$$
$$x_{23} = 331.961623729322$$
$$x_{24} = 89.0117918517108$$
$$x_{25} = 68.0678408277789$$
$$x_{26} = 63.8790506229925$$
$$x_{27} = 101.57816246607$$
$$x_{28} = -99.4837673636768$$
$$x_{29} = 51.3126800086333$$
$$x_{30} = -49.2182849062401$$
$$x_{31} = -36.6519142918809$$
$$x_{32} = 105.766952670856$$
$$x_{33} = 13.6135681655558$$
$$x_{34} = -70.162235930172$$
$$x_{35} = 93.2005820564972$$
$$x_{36} = -82.7286065445312$$
$$x_{37} = -61.7846555205993$$
$$x_{38} = 30.3687289847013$$
Las raíces dadas
$$x_{4} = -346.622389446074$$
$$x_{28} = -99.4837673636768$$
$$x_{7} = -95.2949771588904$$
$$x_{8} = -86.9173967493176$$
$$x_{36} = -82.7286065445312$$
$$x_{18} = -74.3510261349584$$
$$x_{34} = -70.162235930172$$
$$x_{37} = -61.7846555205993$$
$$x_{19} = -57.5958653158129$$
$$x_{30} = -49.2182849062401$$
$$x_{15} = -45.0294947014537$$
$$x_{31} = -36.6519142918809$$
$$x_{2} = -32.4631240870945$$
$$x_{1} = -24.0855436775217$$
$$x_{10} = -19.8967534727354$$
$$x_{17} = -11.5191730631626$$
$$x_{5} = -7.33038285837618$$
$$x_{16} = 1.0471975511966$$
$$x_{13} = 5.23598775598299$$
$$x_{33} = 13.6135681655558$$
$$x_{6} = 17.8023583703422$$
$$x_{3} = 26.1799387799149$$
$$x_{38} = 30.3687289847013$$
$$x_{12} = 38.7463093942741$$
$$x_{20} = 42.9350995990605$$
$$x_{29} = 51.3126800086333$$
$$x_{22} = 55.5014702134197$$
$$x_{26} = 63.8790506229925$$
$$x_{25} = 68.0678408277789$$
$$x_{21} = 76.4454212373516$$
$$x_{9} = 80.634211442138$$
$$x_{24} = 89.0117918517108$$
$$x_{35} = 93.2005820564972$$
$$x_{27} = 101.57816246607$$
$$x_{32} = 105.766952670856$$
$$x_{11} = 114.144533080429$$
$$x_{23} = 331.961623729322$$
$$x_{14} = 59100.6881968824$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{4}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{4} - \frac{1}{10}$$
=
$$-346.622389446074 + - \frac{1}{10}$$
=
$$-346.722389446074$$
lo sustituimos en la expresión
$$\sin{\left(\frac{t}{2} \right)} \leq \frac{1}{2}$$
$$\sin{\left(\frac{t}{2} \right)} \leq \frac{1}{2}$$
Entonces
$$x \leq -346.622389446074$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -346.622389446074 \wedge x \leq -99.4837673636768$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -346.622389446074 \wedge x \leq -99.4837673636768$$
$$x \geq -95.2949771588904 \wedge x \leq -86.9173967493176$$
$$x \geq -82.7286065445312 \wedge x \leq -74.3510261349584$$
$$x \geq -70.162235930172 \wedge x \leq -61.7846555205993$$
$$x \geq -57.5958653158129 \wedge x \leq -49.2182849062401$$
$$x \geq -45.0294947014537 \wedge x \leq -36.6519142918809$$
$$x \geq -32.4631240870945 \wedge x \leq -24.0855436775217$$
$$x \geq -19.8967534727354 \wedge x \leq -11.5191730631626$$
$$x \geq -7.33038285837618 \wedge x \leq 1.0471975511966$$
$$x \geq 5.23598775598299 \wedge x \leq 13.6135681655558$$
$$x \geq 17.8023583703422 \wedge x \leq 26.1799387799149$$
$$x \geq 30.3687289847013 \wedge x \leq 38.7463093942741$$
$$x \geq 42.9350995990605 \wedge x \leq 51.3126800086333$$
$$x \geq 55.5014702134197 \wedge x \leq 63.8790506229925$$
$$x \geq 68.0678408277789 \wedge x \leq 76.4454212373516$$
$$x \geq 80.634211442138 \wedge x \leq 89.0117918517108$$
$$x \geq 93.2005820564972 \wedge x \leq 101.57816246607$$
$$x \geq 105.766952670856 \wedge x \leq 114.144533080429$$
$$x \geq 331.961623729322 \wedge x \leq 59100.6881968824$$
$$\sin{\left(\frac{t}{2} \right)} \leq \frac{1}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\sin{\left(\frac{t}{2} \right)} = \frac{1}{2}$$
Resolvemos:
$$x_{1} = -24.0855436775217$$
$$x_{2} = -32.4631240870945$$
$$x_{3} = 26.1799387799149$$
$$x_{4} = -346.622389446074$$
$$x_{5} = -7.33038285837618$$
$$x_{6} = 17.8023583703422$$
$$x_{7} = -95.2949771588904$$
$$x_{8} = -86.9173967493176$$
$$x_{9} = 80.634211442138$$
$$x_{10} = -19.8967534727354$$
$$x_{11} = 114.144533080429$$
$$x_{12} = 38.7463093942741$$
$$x_{13} = 5.23598775598299$$
$$x_{14} = 59100.6881968824$$
$$x_{15} = -45.0294947014537$$
$$x_{16} = 1.0471975511966$$
$$x_{17} = -11.5191730631626$$
$$x_{18} = -74.3510261349584$$
$$x_{19} = -57.5958653158129$$
$$x_{20} = 42.9350995990605$$
$$x_{21} = 76.4454212373516$$
$$x_{22} = 55.5014702134197$$
$$x_{23} = 331.961623729322$$
$$x_{24} = 89.0117918517108$$
$$x_{25} = 68.0678408277789$$
$$x_{26} = 63.8790506229925$$
$$x_{27} = 101.57816246607$$
$$x_{28} = -99.4837673636768$$
$$x_{29} = 51.3126800086333$$
$$x_{30} = -49.2182849062401$$
$$x_{31} = -36.6519142918809$$
$$x_{32} = 105.766952670856$$
$$x_{33} = 13.6135681655558$$
$$x_{34} = -70.162235930172$$
$$x_{35} = 93.2005820564972$$
$$x_{36} = -82.7286065445312$$
$$x_{37} = -61.7846555205993$$
$$x_{38} = 30.3687289847013$$
$$x_{1} = -24.0855436775217$$
$$x_{2} = -32.4631240870945$$
$$x_{3} = 26.1799387799149$$
$$x_{4} = -346.622389446074$$
$$x_{5} = -7.33038285837618$$
$$x_{6} = 17.8023583703422$$
$$x_{7} = -95.2949771588904$$
$$x_{8} = -86.9173967493176$$
$$x_{9} = 80.634211442138$$
$$x_{10} = -19.8967534727354$$
$$x_{11} = 114.144533080429$$
$$x_{12} = 38.7463093942741$$
$$x_{13} = 5.23598775598299$$
$$x_{14} = 59100.6881968824$$
$$x_{15} = -45.0294947014537$$
$$x_{16} = 1.0471975511966$$
$$x_{17} = -11.5191730631626$$
$$x_{18} = -74.3510261349584$$
$$x_{19} = -57.5958653158129$$
$$x_{20} = 42.9350995990605$$
$$x_{21} = 76.4454212373516$$
$$x_{22} = 55.5014702134197$$
$$x_{23} = 331.961623729322$$
$$x_{24} = 89.0117918517108$$
$$x_{25} = 68.0678408277789$$
$$x_{26} = 63.8790506229925$$
$$x_{27} = 101.57816246607$$
$$x_{28} = -99.4837673636768$$
$$x_{29} = 51.3126800086333$$
$$x_{30} = -49.2182849062401$$
$$x_{31} = -36.6519142918809$$
$$x_{32} = 105.766952670856$$
$$x_{33} = 13.6135681655558$$
$$x_{34} = -70.162235930172$$
$$x_{35} = 93.2005820564972$$
$$x_{36} = -82.7286065445312$$
$$x_{37} = -61.7846555205993$$
$$x_{38} = 30.3687289847013$$
Las raíces dadas
$$x_{4} = -346.622389446074$$
$$x_{28} = -99.4837673636768$$
$$x_{7} = -95.2949771588904$$
$$x_{8} = -86.9173967493176$$
$$x_{36} = -82.7286065445312$$
$$x_{18} = -74.3510261349584$$
$$x_{34} = -70.162235930172$$
$$x_{37} = -61.7846555205993$$
$$x_{19} = -57.5958653158129$$
$$x_{30} = -49.2182849062401$$
$$x_{15} = -45.0294947014537$$
$$x_{31} = -36.6519142918809$$
$$x_{2} = -32.4631240870945$$
$$x_{1} = -24.0855436775217$$
$$x_{10} = -19.8967534727354$$
$$x_{17} = -11.5191730631626$$
$$x_{5} = -7.33038285837618$$
$$x_{16} = 1.0471975511966$$
$$x_{13} = 5.23598775598299$$
$$x_{33} = 13.6135681655558$$
$$x_{6} = 17.8023583703422$$
$$x_{3} = 26.1799387799149$$
$$x_{38} = 30.3687289847013$$
$$x_{12} = 38.7463093942741$$
$$x_{20} = 42.9350995990605$$
$$x_{29} = 51.3126800086333$$
$$x_{22} = 55.5014702134197$$
$$x_{26} = 63.8790506229925$$
$$x_{25} = 68.0678408277789$$
$$x_{21} = 76.4454212373516$$
$$x_{9} = 80.634211442138$$
$$x_{24} = 89.0117918517108$$
$$x_{35} = 93.2005820564972$$
$$x_{27} = 101.57816246607$$
$$x_{32} = 105.766952670856$$
$$x_{11} = 114.144533080429$$
$$x_{23} = 331.961623729322$$
$$x_{14} = 59100.6881968824$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{4}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{4} - \frac{1}{10}$$
=
$$-346.622389446074 + - \frac{1}{10}$$
=
$$-346.722389446074$$
lo sustituimos en la expresión
$$\sin{\left(\frac{t}{2} \right)} \leq \frac{1}{2}$$
$$\sin{\left(\frac{t}{2} \right)} \leq \frac{1}{2}$$
/t\ sin|-| <= 1/2 \2/
Entonces
$$x \leq -346.622389446074$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -346.622389446074 \wedge x \leq -99.4837673636768$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------
x4 x28 x7 x8 x36 x18 x34 x37 x19 x30 x15 x31 x2 x1 x10 x17 x5 x16 x13 x33 x6 x3 x38 x12 x20 x29 x22 x26 x25 x21 x9 x24 x35 x27 x32 x11 x23 x14Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -346.622389446074 \wedge x \leq -99.4837673636768$$
$$x \geq -95.2949771588904 \wedge x \leq -86.9173967493176$$
$$x \geq -82.7286065445312 \wedge x \leq -74.3510261349584$$
$$x \geq -70.162235930172 \wedge x \leq -61.7846555205993$$
$$x \geq -57.5958653158129 \wedge x \leq -49.2182849062401$$
$$x \geq -45.0294947014537 \wedge x \leq -36.6519142918809$$
$$x \geq -32.4631240870945 \wedge x \leq -24.0855436775217$$
$$x \geq -19.8967534727354 \wedge x \leq -11.5191730631626$$
$$x \geq -7.33038285837618 \wedge x \leq 1.0471975511966$$
$$x \geq 5.23598775598299 \wedge x \leq 13.6135681655558$$
$$x \geq 17.8023583703422 \wedge x \leq 26.1799387799149$$
$$x \geq 30.3687289847013 \wedge x \leq 38.7463093942741$$
$$x \geq 42.9350995990605 \wedge x \leq 51.3126800086333$$
$$x \geq 55.5014702134197 \wedge x \leq 63.8790506229925$$
$$x \geq 68.0678408277789 \wedge x \leq 76.4454212373516$$
$$x \geq 80.634211442138 \wedge x \leq 89.0117918517108$$
$$x \geq 93.2005820564972 \wedge x \leq 101.57816246607$$
$$x \geq 105.766952670856 \wedge x \leq 114.144533080429$$
$$x \geq 331.961623729322 \wedge x \leq 59100.6881968824$$
Respuesta rápida
[src]
/ / pi\ /5*pi \\ Or|And|0 <= t, t <= --|, And|---- <= t, t <= 4*pi|| \ \ 3 / \ 3 //
$$\left(0 \leq t \wedge t \leq \frac{\pi}{3}\right) \vee \left(\frac{5 \pi}{3} \leq t \wedge t \leq 4 \pi\right)$$
((0 <= t)∧(t <= pi/3))∨((5*pi/3 <= t)∧(t <= 4*pi))
Respuesta rápida 2
[src]
pi 5*pi
[0, --] U [----, 4*pi]
3 3
$$x\ in\ \left[0, \frac{\pi}{3}\right] \cup \left[\frac{5 \pi}{3}, 4 \pi\right]$$
x in Union(Interval(0, pi/3), Interval(5*pi/3, 4*pi))