Mister Exam
cost≤1/2 inequation
The solution
Detail solution
Given the inequality:
$$\cos{\left(t \right)} \leq \frac{1}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(t \right)} = \frac{1}{2}$$
Solve:
Given the equation
$$\cos{\left(t \right)} = \frac{1}{2}$$
transform
$$\cos{\left(t \right)} - \frac{1}{2} = 0$$
$$\cos{\left(t \right)} - \frac{1}{2} = 0$$
Do replacement
$$w = \cos{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{2}$$
We get the answer: w = 1/2
do backward replacement
$$\cos{\left(t \right)} = w$$
substitute w:
$$x_{1} = 38.7463093942741$$
$$x_{2} = 13.6135681655558$$
$$x_{3} = 11.5191730631626$$
$$x_{4} = -55.5014702134197$$
$$x_{5} = -30.3687289847013$$
$$x_{6} = -61.7846555205993$$
$$x_{7} = -86.9173967493176$$
$$x_{8} = 89.0117918517108$$
$$x_{9} = -51.3126800086333$$
$$x_{10} = 1.0471975511966$$
$$x_{11} = -68.0678408277789$$
$$x_{12} = 36.6519142918809$$
$$x_{13} = -70.162235930172$$
$$x_{14} = 93.2005820564972$$
$$x_{15} = -95.2949771588904$$
$$x_{16} = 49.2182849062401$$
$$x_{17} = 30.3687289847013$$
$$x_{18} = 17.8023583703422$$
$$x_{19} = -32.4631240870945$$
$$x_{20} = -99.4837673636768$$
$$x_{21} = 63.8790506229925$$
$$x_{22} = 42.9350995990605$$
$$x_{23} = -225.147473507269$$
$$x_{24} = -93.2005820564972$$
$$x_{25} = -17.8023583703422$$
$$x_{26} = 7.33038285837618$$
$$x_{27} = -11.5191730631626$$
$$x_{28} = 57.5958653158129$$
$$x_{29} = -42.9350995990605$$
$$x_{30} = -24.0855436775217$$
$$x_{31} = 70.162235930172$$
$$x_{32} = -36.6519142918809$$
$$x_{33} = -26.1799387799149$$
$$x_{34} = 19.8967534727354$$
$$x_{35} = -76.4454212373516$$
$$x_{36} = 76.4454212373516$$
$$x_{37} = -1.0471975511966$$
$$x_{38} = 1651.43053823704$$
$$x_{39} = 55.5014702134197$$
$$x_{40} = -5.23598775598299$$
$$x_{41} = 51.3126800086333$$
$$x_{42} = 45.0294947014537$$
$$x_{43} = 68.0678408277789$$
$$x_{44} = -45.0294947014537$$
$$x_{45} = -82.7286065445312$$
$$x_{46} = -19.8967534727354$$
$$x_{47} = -57.5958653158129$$
$$x_{48} = 74.3510261349584$$
$$x_{49} = -38.7463093942741$$
$$x_{50} = 80.634211442138$$
$$x_{51} = 99.4837673636768$$
$$x_{52} = -359.188760060433$$
$$x_{53} = 26.1799387799149$$
$$x_{54} = -63.8790506229925$$
$$x_{55} = 5.23598775598299$$
$$x_{56} = -89.0117918517108$$
$$x_{57} = 82.7286065445312$$
$$x_{58} = -13.6135681655558$$
$$x_{59} = -80.634211442138$$
$$x_{60} = -74.3510261349584$$
$$x_{61} = 86.9173967493176$$
$$x_{62} = 24.0855436775217$$
$$x_{63} = -49.2182849062401$$
$$x_{64} = 61.7846555205993$$
$$x_{65} = 95.2949771588904$$
$$x_{66} = 32.4631240870945$$
$$x_{67} = -7.33038285837618$$
$$x_{1} = 38.7463093942741$$
$$x_{2} = 13.6135681655558$$
$$x_{3} = 11.5191730631626$$
$$x_{4} = -55.5014702134197$$
$$x_{5} = -30.3687289847013$$
$$x_{6} = -61.7846555205993$$
$$x_{7} = -86.9173967493176$$
$$x_{8} = 89.0117918517108$$
$$x_{9} = -51.3126800086333$$
$$x_{10} = 1.0471975511966$$
$$x_{11} = -68.0678408277789$$
$$x_{12} = 36.6519142918809$$
$$x_{13} = -70.162235930172$$
$$x_{14} = 93.2005820564972$$
$$x_{15} = -95.2949771588904$$
$$x_{16} = 49.2182849062401$$
$$x_{17} = 30.3687289847013$$
$$x_{18} = 17.8023583703422$$
$$x_{19} = -32.4631240870945$$
$$x_{20} = -99.4837673636768$$
$$x_{21} = 63.8790506229925$$
$$x_{22} = 42.9350995990605$$
$$x_{23} = -225.147473507269$$
$$x_{24} = -93.2005820564972$$
$$x_{25} = -17.8023583703422$$
$$x_{26} = 7.33038285837618$$
$$x_{27} = -11.5191730631626$$
$$x_{28} = 57.5958653158129$$
$$x_{29} = -42.9350995990605$$
$$x_{30} = -24.0855436775217$$
$$x_{31} = 70.162235930172$$
$$x_{32} = -36.6519142918809$$
$$x_{33} = -26.1799387799149$$
$$x_{34} = 19.8967534727354$$
$$x_{35} = -76.4454212373516$$
$$x_{36} = 76.4454212373516$$
$$x_{37} = -1.0471975511966$$
$$x_{38} = 1651.43053823704$$
$$x_{39} = 55.5014702134197$$
$$x_{40} = -5.23598775598299$$
$$x_{41} = 51.3126800086333$$
$$x_{42} = 45.0294947014537$$
$$x_{43} = 68.0678408277789$$
$$x_{44} = -45.0294947014537$$
$$x_{45} = -82.7286065445312$$
$$x_{46} = -19.8967534727354$$
$$x_{47} = -57.5958653158129$$
$$x_{48} = 74.3510261349584$$
$$x_{49} = -38.7463093942741$$
$$x_{50} = 80.634211442138$$
$$x_{51} = 99.4837673636768$$
$$x_{52} = -359.188760060433$$
$$x_{53} = 26.1799387799149$$
$$x_{54} = -63.8790506229925$$
$$x_{55} = 5.23598775598299$$
$$x_{56} = -89.0117918517108$$
$$x_{57} = 82.7286065445312$$
$$x_{58} = -13.6135681655558$$
$$x_{59} = -80.634211442138$$
$$x_{60} = -74.3510261349584$$
$$x_{61} = 86.9173967493176$$
$$x_{62} = 24.0855436775217$$
$$x_{63} = -49.2182849062401$$
$$x_{64} = 61.7846555205993$$
$$x_{65} = 95.2949771588904$$
$$x_{66} = 32.4631240870945$$
$$x_{67} = -7.33038285837618$$
This roots
$$x_{52} = -359.188760060433$$
$$x_{23} = -225.147473507269$$
$$x_{20} = -99.4837673636768$$
$$x_{15} = -95.2949771588904$$
$$x_{24} = -93.2005820564972$$
$$x_{56} = -89.0117918517108$$
$$x_{7} = -86.9173967493176$$
$$x_{45} = -82.7286065445312$$
$$x_{59} = -80.634211442138$$
$$x_{35} = -76.4454212373516$$
$$x_{60} = -74.3510261349584$$
$$x_{13} = -70.162235930172$$
$$x_{11} = -68.0678408277789$$
$$x_{54} = -63.8790506229925$$
$$x_{6} = -61.7846555205993$$
$$x_{47} = -57.5958653158129$$
$$x_{4} = -55.5014702134197$$
$$x_{9} = -51.3126800086333$$
$$x_{63} = -49.2182849062401$$
$$x_{44} = -45.0294947014537$$
$$x_{29} = -42.9350995990605$$
$$x_{49} = -38.7463093942741$$
$$x_{32} = -36.6519142918809$$
$$x_{19} = -32.4631240870945$$
$$x_{5} = -30.3687289847013$$
$$x_{33} = -26.1799387799149$$
$$x_{30} = -24.0855436775217$$
$$x_{46} = -19.8967534727354$$
$$x_{25} = -17.8023583703422$$
$$x_{58} = -13.6135681655558$$
$$x_{27} = -11.5191730631626$$
$$x_{67} = -7.33038285837618$$
$$x_{40} = -5.23598775598299$$
$$x_{37} = -1.0471975511966$$
$$x_{10} = 1.0471975511966$$
$$x_{55} = 5.23598775598299$$
$$x_{26} = 7.33038285837618$$
$$x_{3} = 11.5191730631626$$
$$x_{2} = 13.6135681655558$$
$$x_{18} = 17.8023583703422$$
$$x_{34} = 19.8967534727354$$
$$x_{62} = 24.0855436775217$$
$$x_{53} = 26.1799387799149$$
$$x_{17} = 30.3687289847013$$
$$x_{66} = 32.4631240870945$$
$$x_{12} = 36.6519142918809$$
$$x_{1} = 38.7463093942741$$
$$x_{22} = 42.9350995990605$$
$$x_{42} = 45.0294947014537$$
$$x_{16} = 49.2182849062401$$
$$x_{41} = 51.3126800086333$$
$$x_{39} = 55.5014702134197$$
$$x_{28} = 57.5958653158129$$
$$x_{64} = 61.7846555205993$$
$$x_{21} = 63.8790506229925$$
$$x_{43} = 68.0678408277789$$
$$x_{31} = 70.162235930172$$
$$x_{48} = 74.3510261349584$$
$$x_{36} = 76.4454212373516$$
$$x_{50} = 80.634211442138$$
$$x_{57} = 82.7286065445312$$
$$x_{61} = 86.9173967493176$$
$$x_{8} = 89.0117918517108$$
$$x_{14} = 93.2005820564972$$
$$x_{65} = 95.2949771588904$$
$$x_{51} = 99.4837673636768$$
$$x_{38} = 1651.43053823704$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{52}$$
For example, let's take the point
$$x_{0} = x_{52} - \frac{1}{10}$$
=
$$-359.188760060433 + - \frac{1}{10}$$
=
$$-359.288760060433$$
substitute to the expression
$$\cos{\left(t \right)} \leq \frac{1}{2}$$
$$\cos{\left(t \right)} \leq \frac{1}{2}$$
Then
$$x \leq -359.188760060433$$
no execute
one of the solutions of our inequality is:
$$x \geq -359.188760060433 \wedge x \leq -225.147473507269$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \geq -359.188760060433 \wedge x \leq -225.147473507269$$
$$x \geq -99.4837673636768 \wedge x \leq -95.2949771588904$$
$$x \geq -93.2005820564972 \wedge x \leq -89.0117918517108$$
$$x \geq -86.9173967493176 \wedge x \leq -82.7286065445312$$
$$x \geq -80.634211442138 \wedge x \leq -76.4454212373516$$
$$x \geq -74.3510261349584 \wedge x \leq -70.162235930172$$
$$x \geq -68.0678408277789 \wedge x \leq -63.8790506229925$$
$$x \geq -61.7846555205993 \wedge x \leq -57.5958653158129$$
$$x \geq -55.5014702134197 \wedge x \leq -51.3126800086333$$
$$x \geq -49.2182849062401 \wedge x \leq -45.0294947014537$$
$$x \geq -42.9350995990605 \wedge x \leq -38.7463093942741$$
$$x \geq -36.6519142918809 \wedge x \leq -32.4631240870945$$
$$x \geq -30.3687289847013 \wedge x \leq -26.1799387799149$$
$$x \geq -24.0855436775217 \wedge x \leq -19.8967534727354$$
$$x \geq -17.8023583703422 \wedge x \leq -13.6135681655558$$
$$x \geq -11.5191730631626 \wedge x \leq -7.33038285837618$$
$$x \geq -5.23598775598299 \wedge x \leq -1.0471975511966$$
$$x \geq 1.0471975511966 \wedge x \leq 5.23598775598299$$
$$x \geq 7.33038285837618 \wedge x \leq 11.5191730631626$$
$$x \geq 13.6135681655558 \wedge x \leq 17.8023583703422$$
$$x \geq 19.8967534727354 \wedge x \leq 24.0855436775217$$
$$x \geq 26.1799387799149 \wedge x \leq 30.3687289847013$$
$$x \geq 32.4631240870945 \wedge x \leq 36.6519142918809$$
$$x \geq 38.7463093942741 \wedge x \leq 42.9350995990605$$
$$x \geq 45.0294947014537 \wedge x \leq 49.2182849062401$$
$$x \geq 51.3126800086333 \wedge x \leq 55.5014702134197$$
$$x \geq 57.5958653158129 \wedge x \leq 61.7846555205993$$
$$x \geq 63.8790506229925 \wedge x \leq 68.0678408277789$$
$$x \geq 70.162235930172 \wedge x \leq 74.3510261349584$$
$$x \geq 76.4454212373516 \wedge x \leq 80.634211442138$$
$$x \geq 82.7286065445312 \wedge x \leq 86.9173967493176$$
$$x \geq 89.0117918517108 \wedge x \leq 93.2005820564972$$
$$x \geq 95.2949771588904 \wedge x \leq 99.4837673636768$$
$$x \geq 1651.43053823704$$
$$\cos{\left(t \right)} \leq \frac{1}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\cos{\left(t \right)} = \frac{1}{2}$$
Solve:
Given the equation
$$\cos{\left(t \right)} = \frac{1}{2}$$
transform
$$\cos{\left(t \right)} - \frac{1}{2} = 0$$
$$\cos{\left(t \right)} - \frac{1}{2} = 0$$
Do replacement
$$w = \cos{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{2}$$
We get the answer: w = 1/2
do backward replacement
$$\cos{\left(t \right)} = w$$
substitute w:
$$x_{1} = 38.7463093942741$$
$$x_{2} = 13.6135681655558$$
$$x_{3} = 11.5191730631626$$
$$x_{4} = -55.5014702134197$$
$$x_{5} = -30.3687289847013$$
$$x_{6} = -61.7846555205993$$
$$x_{7} = -86.9173967493176$$
$$x_{8} = 89.0117918517108$$
$$x_{9} = -51.3126800086333$$
$$x_{10} = 1.0471975511966$$
$$x_{11} = -68.0678408277789$$
$$x_{12} = 36.6519142918809$$
$$x_{13} = -70.162235930172$$
$$x_{14} = 93.2005820564972$$
$$x_{15} = -95.2949771588904$$
$$x_{16} = 49.2182849062401$$
$$x_{17} = 30.3687289847013$$
$$x_{18} = 17.8023583703422$$
$$x_{19} = -32.4631240870945$$
$$x_{20} = -99.4837673636768$$
$$x_{21} = 63.8790506229925$$
$$x_{22} = 42.9350995990605$$
$$x_{23} = -225.147473507269$$
$$x_{24} = -93.2005820564972$$
$$x_{25} = -17.8023583703422$$
$$x_{26} = 7.33038285837618$$
$$x_{27} = -11.5191730631626$$
$$x_{28} = 57.5958653158129$$
$$x_{29} = -42.9350995990605$$
$$x_{30} = -24.0855436775217$$
$$x_{31} = 70.162235930172$$
$$x_{32} = -36.6519142918809$$
$$x_{33} = -26.1799387799149$$
$$x_{34} = 19.8967534727354$$
$$x_{35} = -76.4454212373516$$
$$x_{36} = 76.4454212373516$$
$$x_{37} = -1.0471975511966$$
$$x_{38} = 1651.43053823704$$
$$x_{39} = 55.5014702134197$$
$$x_{40} = -5.23598775598299$$
$$x_{41} = 51.3126800086333$$
$$x_{42} = 45.0294947014537$$
$$x_{43} = 68.0678408277789$$
$$x_{44} = -45.0294947014537$$
$$x_{45} = -82.7286065445312$$
$$x_{46} = -19.8967534727354$$
$$x_{47} = -57.5958653158129$$
$$x_{48} = 74.3510261349584$$
$$x_{49} = -38.7463093942741$$
$$x_{50} = 80.634211442138$$
$$x_{51} = 99.4837673636768$$
$$x_{52} = -359.188760060433$$
$$x_{53} = 26.1799387799149$$
$$x_{54} = -63.8790506229925$$
$$x_{55} = 5.23598775598299$$
$$x_{56} = -89.0117918517108$$
$$x_{57} = 82.7286065445312$$
$$x_{58} = -13.6135681655558$$
$$x_{59} = -80.634211442138$$
$$x_{60} = -74.3510261349584$$
$$x_{61} = 86.9173967493176$$
$$x_{62} = 24.0855436775217$$
$$x_{63} = -49.2182849062401$$
$$x_{64} = 61.7846555205993$$
$$x_{65} = 95.2949771588904$$
$$x_{66} = 32.4631240870945$$
$$x_{67} = -7.33038285837618$$
$$x_{1} = 38.7463093942741$$
$$x_{2} = 13.6135681655558$$
$$x_{3} = 11.5191730631626$$
$$x_{4} = -55.5014702134197$$
$$x_{5} = -30.3687289847013$$
$$x_{6} = -61.7846555205993$$
$$x_{7} = -86.9173967493176$$
$$x_{8} = 89.0117918517108$$
$$x_{9} = -51.3126800086333$$
$$x_{10} = 1.0471975511966$$
$$x_{11} = -68.0678408277789$$
$$x_{12} = 36.6519142918809$$
$$x_{13} = -70.162235930172$$
$$x_{14} = 93.2005820564972$$
$$x_{15} = -95.2949771588904$$
$$x_{16} = 49.2182849062401$$
$$x_{17} = 30.3687289847013$$
$$x_{18} = 17.8023583703422$$
$$x_{19} = -32.4631240870945$$
$$x_{20} = -99.4837673636768$$
$$x_{21} = 63.8790506229925$$
$$x_{22} = 42.9350995990605$$
$$x_{23} = -225.147473507269$$
$$x_{24} = -93.2005820564972$$
$$x_{25} = -17.8023583703422$$
$$x_{26} = 7.33038285837618$$
$$x_{27} = -11.5191730631626$$
$$x_{28} = 57.5958653158129$$
$$x_{29} = -42.9350995990605$$
$$x_{30} = -24.0855436775217$$
$$x_{31} = 70.162235930172$$
$$x_{32} = -36.6519142918809$$
$$x_{33} = -26.1799387799149$$
$$x_{34} = 19.8967534727354$$
$$x_{35} = -76.4454212373516$$
$$x_{36} = 76.4454212373516$$
$$x_{37} = -1.0471975511966$$
$$x_{38} = 1651.43053823704$$
$$x_{39} = 55.5014702134197$$
$$x_{40} = -5.23598775598299$$
$$x_{41} = 51.3126800086333$$
$$x_{42} = 45.0294947014537$$
$$x_{43} = 68.0678408277789$$
$$x_{44} = -45.0294947014537$$
$$x_{45} = -82.7286065445312$$
$$x_{46} = -19.8967534727354$$
$$x_{47} = -57.5958653158129$$
$$x_{48} = 74.3510261349584$$
$$x_{49} = -38.7463093942741$$
$$x_{50} = 80.634211442138$$
$$x_{51} = 99.4837673636768$$
$$x_{52} = -359.188760060433$$
$$x_{53} = 26.1799387799149$$
$$x_{54} = -63.8790506229925$$
$$x_{55} = 5.23598775598299$$
$$x_{56} = -89.0117918517108$$
$$x_{57} = 82.7286065445312$$
$$x_{58} = -13.6135681655558$$
$$x_{59} = -80.634211442138$$
$$x_{60} = -74.3510261349584$$
$$x_{61} = 86.9173967493176$$
$$x_{62} = 24.0855436775217$$
$$x_{63} = -49.2182849062401$$
$$x_{64} = 61.7846555205993$$
$$x_{65} = 95.2949771588904$$
$$x_{66} = 32.4631240870945$$
$$x_{67} = -7.33038285837618$$
This roots
$$x_{52} = -359.188760060433$$
$$x_{23} = -225.147473507269$$
$$x_{20} = -99.4837673636768$$
$$x_{15} = -95.2949771588904$$
$$x_{24} = -93.2005820564972$$
$$x_{56} = -89.0117918517108$$
$$x_{7} = -86.9173967493176$$
$$x_{45} = -82.7286065445312$$
$$x_{59} = -80.634211442138$$
$$x_{35} = -76.4454212373516$$
$$x_{60} = -74.3510261349584$$
$$x_{13} = -70.162235930172$$
$$x_{11} = -68.0678408277789$$
$$x_{54} = -63.8790506229925$$
$$x_{6} = -61.7846555205993$$
$$x_{47} = -57.5958653158129$$
$$x_{4} = -55.5014702134197$$
$$x_{9} = -51.3126800086333$$
$$x_{63} = -49.2182849062401$$
$$x_{44} = -45.0294947014537$$
$$x_{29} = -42.9350995990605$$
$$x_{49} = -38.7463093942741$$
$$x_{32} = -36.6519142918809$$
$$x_{19} = -32.4631240870945$$
$$x_{5} = -30.3687289847013$$
$$x_{33} = -26.1799387799149$$
$$x_{30} = -24.0855436775217$$
$$x_{46} = -19.8967534727354$$
$$x_{25} = -17.8023583703422$$
$$x_{58} = -13.6135681655558$$
$$x_{27} = -11.5191730631626$$
$$x_{67} = -7.33038285837618$$
$$x_{40} = -5.23598775598299$$
$$x_{37} = -1.0471975511966$$
$$x_{10} = 1.0471975511966$$
$$x_{55} = 5.23598775598299$$
$$x_{26} = 7.33038285837618$$
$$x_{3} = 11.5191730631626$$
$$x_{2} = 13.6135681655558$$
$$x_{18} = 17.8023583703422$$
$$x_{34} = 19.8967534727354$$
$$x_{62} = 24.0855436775217$$
$$x_{53} = 26.1799387799149$$
$$x_{17} = 30.3687289847013$$
$$x_{66} = 32.4631240870945$$
$$x_{12} = 36.6519142918809$$
$$x_{1} = 38.7463093942741$$
$$x_{22} = 42.9350995990605$$
$$x_{42} = 45.0294947014537$$
$$x_{16} = 49.2182849062401$$
$$x_{41} = 51.3126800086333$$
$$x_{39} = 55.5014702134197$$
$$x_{28} = 57.5958653158129$$
$$x_{64} = 61.7846555205993$$
$$x_{21} = 63.8790506229925$$
$$x_{43} = 68.0678408277789$$
$$x_{31} = 70.162235930172$$
$$x_{48} = 74.3510261349584$$
$$x_{36} = 76.4454212373516$$
$$x_{50} = 80.634211442138$$
$$x_{57} = 82.7286065445312$$
$$x_{61} = 86.9173967493176$$
$$x_{8} = 89.0117918517108$$
$$x_{14} = 93.2005820564972$$
$$x_{65} = 95.2949771588904$$
$$x_{51} = 99.4837673636768$$
$$x_{38} = 1651.43053823704$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{52}$$
For example, let's take the point
$$x_{0} = x_{52} - \frac{1}{10}$$
=
$$-359.188760060433 + - \frac{1}{10}$$
=
$$-359.288760060433$$
substitute to the expression
$$\cos{\left(t \right)} \leq \frac{1}{2}$$
$$\cos{\left(t \right)} \leq \frac{1}{2}$$
cos(t) <= 1/2
Then
$$x \leq -359.188760060433$$
no execute
one of the solutions of our inequality is:
$$x \geq -359.188760060433 \wedge x \leq -225.147473507269$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
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x52 x23 x20 x15 x24 x56 x7 x45 x59 x35 x60 x13 x11 x54 x6 x47 x4 x9 x63 x44 x29 x49 x32 x19 x5 x33 x30 x46 x25 x58 x27 x67 x40 x37 x10 x55 x26 x3 x2 x18 x34 x62 x53 x17 x66 x12 x1 x22 x42 x16 x41 x39 x28 x64 x21 x43 x31 x48 x36 x50 x57 x61 x8 x14 x65 x51 x38Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \geq -359.188760060433 \wedge x \leq -225.147473507269$$
$$x \geq -99.4837673636768 \wedge x \leq -95.2949771588904$$
$$x \geq -93.2005820564972 \wedge x \leq -89.0117918517108$$
$$x \geq -86.9173967493176 \wedge x \leq -82.7286065445312$$
$$x \geq -80.634211442138 \wedge x \leq -76.4454212373516$$
$$x \geq -74.3510261349584 \wedge x \leq -70.162235930172$$
$$x \geq -68.0678408277789 \wedge x \leq -63.8790506229925$$
$$x \geq -61.7846555205993 \wedge x \leq -57.5958653158129$$
$$x \geq -55.5014702134197 \wedge x \leq -51.3126800086333$$
$$x \geq -49.2182849062401 \wedge x \leq -45.0294947014537$$
$$x \geq -42.9350995990605 \wedge x \leq -38.7463093942741$$
$$x \geq -36.6519142918809 \wedge x \leq -32.4631240870945$$
$$x \geq -30.3687289847013 \wedge x \leq -26.1799387799149$$
$$x \geq -24.0855436775217 \wedge x \leq -19.8967534727354$$
$$x \geq -17.8023583703422 \wedge x \leq -13.6135681655558$$
$$x \geq -11.5191730631626 \wedge x \leq -7.33038285837618$$
$$x \geq -5.23598775598299 \wedge x \leq -1.0471975511966$$
$$x \geq 1.0471975511966 \wedge x \leq 5.23598775598299$$
$$x \geq 7.33038285837618 \wedge x \leq 11.5191730631626$$
$$x \geq 13.6135681655558 \wedge x \leq 17.8023583703422$$
$$x \geq 19.8967534727354 \wedge x \leq 24.0855436775217$$
$$x \geq 26.1799387799149 \wedge x \leq 30.3687289847013$$
$$x \geq 32.4631240870945 \wedge x \leq 36.6519142918809$$
$$x \geq 38.7463093942741 \wedge x \leq 42.9350995990605$$
$$x \geq 45.0294947014537 \wedge x \leq 49.2182849062401$$
$$x \geq 51.3126800086333 \wedge x \leq 55.5014702134197$$
$$x \geq 57.5958653158129 \wedge x \leq 61.7846555205993$$
$$x \geq 63.8790506229925 \wedge x \leq 68.0678408277789$$
$$x \geq 70.162235930172 \wedge x \leq 74.3510261349584$$
$$x \geq 76.4454212373516 \wedge x \leq 80.634211442138$$
$$x \geq 82.7286065445312 \wedge x \leq 86.9173967493176$$
$$x \geq 89.0117918517108 \wedge x \leq 93.2005820564972$$
$$x \geq 95.2949771588904 \wedge x \leq 99.4837673636768$$
$$x \geq 1651.43053823704$$
Rapid solution 2
[src]
pi 5*pi [--, ----] 3 3
$$x\ in\ \left[\frac{\pi}{3}, \frac{5 \pi}{3}\right]$$
x in Interval(pi/3, 5*pi/3)
Rapid solution
[src]
/pi 5*pi\ And|-- <= t, t <= ----| \3 3 /
$$\frac{\pi}{3} \leq t \wedge t \leq \frac{5 \pi}{3}$$
(pi/3 <= t)∧(t <= 5*pi/3)