Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- 8x<=-3(1-x^2)
- 0,5*(4^x+6)>1
- -5/(x-2)^2<0
- (5x-7)/4>0
- Derivative of:
-
cos(t)
-
0,5
- Limit of the function:
-
cos(t)
- Integral of d{x}:
- cos(t)
- 0,5
- Sum of series:
-
0,5
-
Identical expressions
- cos(t)< zero , five
- co sinus of e of (t) less than 0,5
- co sinus of e of (t) less than zero , five
- cost<0,5
-
Similar expressions
- cost>1/2
- cost<√2/2
- cost<=-3/2
cos(t)<0,5 inequation
The solution
Detail solution
Given the inequality:
$$\cos{\left(t \right)} < \frac{1}{2}$$
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:
$$x_{1} = -61.7846555205993$$
$$x_{2} = 17.8023583703422$$
$$x_{3} = 99.4837673636768$$
$$x_{4} = -225.147473507269$$
$$x_{5} = 80.634211442138$$
$$x_{6} = 63.8790506229925$$
$$x_{7} = -86.9173967493176$$
$$x_{8} = 95.2949771588904$$
$$x_{9} = -45.0294947014537$$
$$x_{10} = 70.162235930172$$
$$x_{11} = -26.1799387799149$$
$$x_{12} = -99.4837673636768$$
$$x_{13} = -38.7463093942741$$
$$x_{14} = 13.6135681655558$$
$$x_{15} = 24.0855436775217$$
$$x_{16} = 82.7286065445312$$
$$x_{17} = -17.8023583703422$$
$$x_{18} = 93.2005820564972$$
$$x_{19} = -80.634211442138$$
$$x_{20} = -42.9350995990605$$
$$x_{21} = 68.0678408277789$$
$$x_{22} = -49.2182849062401$$
$$x_{23} = -13.6135681655558$$
$$x_{24} = 32.4631240870945$$
$$x_{25} = -57.5958653158129$$
$$x_{26} = 74.3510261349584$$
$$x_{27} = 86.9173967493176$$
$$x_{28} = -359.188760060433$$
$$x_{29} = -55.5014702134197$$
$$x_{30} = -68.0678408277789$$
$$x_{31} = 51.3126800086333$$
$$x_{32} = 36.6519142918809$$
$$x_{33} = 7.33038285837618$$
$$x_{34} = 19.8967534727354$$
$$x_{35} = 76.4454212373516$$
$$x_{36} = 38.7463093942741$$
$$x_{37} = -32.4631240870945$$
$$x_{38} = 55.5014702134197$$
$$x_{39} = -51.3126800086333$$
$$x_{40} = -5.23598775598299$$
$$x_{41} = 30.3687289847013$$
$$x_{42} = -19.8967534727354$$
$$x_{43} = 57.5958653158129$$
$$x_{44} = 61.7846555205993$$
$$x_{45} = 5.23598775598299$$
$$x_{46} = -11.5191730631626$$
$$x_{47} = 1651.43053823704$$
$$x_{48} = -7.33038285837618$$
$$x_{49} = -1.0471975511966$$
$$x_{50} = -30.3687289847013$$
$$x_{51} = -70.162235930172$$
$$x_{52} = -93.2005820564972$$
$$x_{53} = -24.0855436775217$$
$$x_{54} = -95.2949771588904$$
$$x_{55} = 11.5191730631626$$
$$x_{56} = -89.0117918517108$$
$$x_{57} = -63.8790506229925$$
$$x_{58} = 49.2182849062401$$
$$x_{59} = 42.9350995990605$$
$$x_{60} = -76.4454212373516$$
$$x_{61} = 45.0294947014537$$
$$x_{62} = 1.0471975511966$$
$$x_{63} = 26.1799387799149$$
$$x_{64} = 89.0117918517108$$
$$x_{65} = -36.6519142918809$$
$$x_{66} = -82.7286065445312$$
$$x_{67} = -74.3510261349584$$
$$x_{1} = -61.7846555205993$$
$$x_{2} = 17.8023583703422$$
$$x_{3} = 99.4837673636768$$
$$x_{4} = -225.147473507269$$
$$x_{5} = 80.634211442138$$
$$x_{6} = 63.8790506229925$$
$$x_{7} = -86.9173967493176$$
$$x_{8} = 95.2949771588904$$
$$x_{9} = -45.0294947014537$$
$$x_{10} = 70.162235930172$$
$$x_{11} = -26.1799387799149$$
$$x_{12} = -99.4837673636768$$
$$x_{13} = -38.7463093942741$$
$$x_{14} = 13.6135681655558$$
$$x_{15} = 24.0855436775217$$
$$x_{16} = 82.7286065445312$$
$$x_{17} = -17.8023583703422$$
$$x_{18} = 93.2005820564972$$
$$x_{19} = -80.634211442138$$
$$x_{20} = -42.9350995990605$$
$$x_{21} = 68.0678408277789$$
$$x_{22} = -49.2182849062401$$
$$x_{23} = -13.6135681655558$$
$$x_{24} = 32.4631240870945$$
$$x_{25} = -57.5958653158129$$
$$x_{26} = 74.3510261349584$$
$$x_{27} = 86.9173967493176$$
$$x_{28} = -359.188760060433$$
$$x_{29} = -55.5014702134197$$
$$x_{30} = -68.0678408277789$$
$$x_{31} = 51.3126800086333$$
$$x_{32} = 36.6519142918809$$
$$x_{33} = 7.33038285837618$$
$$x_{34} = 19.8967534727354$$
$$x_{35} = 76.4454212373516$$
$$x_{36} = 38.7463093942741$$
$$x_{37} = -32.4631240870945$$
$$x_{38} = 55.5014702134197$$
$$x_{39} = -51.3126800086333$$
$$x_{40} = -5.23598775598299$$
$$x_{41} = 30.3687289847013$$
$$x_{42} = -19.8967534727354$$
$$x_{43} = 57.5958653158129$$
$$x_{44} = 61.7846555205993$$
$$x_{45} = 5.23598775598299$$
$$x_{46} = -11.5191730631626$$
$$x_{47} = 1651.43053823704$$
$$x_{48} = -7.33038285837618$$
$$x_{49} = -1.0471975511966$$
$$x_{50} = -30.3687289847013$$
$$x_{51} = -70.162235930172$$
$$x_{52} = -93.2005820564972$$
$$x_{53} = -24.0855436775217$$
$$x_{54} = -95.2949771588904$$
$$x_{55} = 11.5191730631626$$
$$x_{56} = -89.0117918517108$$
$$x_{57} = -63.8790506229925$$
$$x_{58} = 49.2182849062401$$
$$x_{59} = 42.9350995990605$$
$$x_{60} = -76.4454212373516$$
$$x_{61} = 45.0294947014537$$
$$x_{62} = 1.0471975511966$$
$$x_{63} = 26.1799387799149$$
$$x_{64} = 89.0117918517108$$
$$x_{65} = -36.6519142918809$$
$$x_{66} = -82.7286065445312$$
$$x_{67} = -74.3510261349584$$
This roots
$$x_{28} = -359.188760060433$$
$$x_{4} = -225.147473507269$$
$$x_{12} = -99.4837673636768$$
$$x_{54} = -95.2949771588904$$
$$x_{52} = -93.2005820564972$$
$$x_{56} = -89.0117918517108$$
$$x_{7} = -86.9173967493176$$
$$x_{66} = -82.7286065445312$$
$$x_{19} = -80.634211442138$$
$$x_{60} = -76.4454212373516$$
$$x_{67} = -74.3510261349584$$
$$x_{51} = -70.162235930172$$
$$x_{30} = -68.0678408277789$$
$$x_{57} = -63.8790506229925$$
$$x_{1} = -61.7846555205993$$
$$x_{25} = -57.5958653158129$$
$$x_{29} = -55.5014702134197$$
$$x_{39} = -51.3126800086333$$
$$x_{22} = -49.2182849062401$$
$$x_{9} = -45.0294947014537$$
$$x_{20} = -42.9350995990605$$
$$x_{13} = -38.7463093942741$$
$$x_{65} = -36.6519142918809$$
$$x_{37} = -32.4631240870945$$
$$x_{50} = -30.3687289847013$$
$$x_{11} = -26.1799387799149$$
$$x_{53} = -24.0855436775217$$
$$x_{42} = -19.8967534727354$$
$$x_{17} = -17.8023583703422$$
$$x_{23} = -13.6135681655558$$
$$x_{46} = -11.5191730631626$$
$$x_{48} = -7.33038285837618$$
$$x_{40} = -5.23598775598299$$
$$x_{49} = -1.0471975511966$$
$$x_{62} = 1.0471975511966$$
$$x_{45} = 5.23598775598299$$
$$x_{33} = 7.33038285837618$$
$$x_{55} = 11.5191730631626$$
$$x_{14} = 13.6135681655558$$
$$x_{2} = 17.8023583703422$$
$$x_{34} = 19.8967534727354$$
$$x_{15} = 24.0855436775217$$
$$x_{63} = 26.1799387799149$$
$$x_{41} = 30.3687289847013$$
$$x_{24} = 32.4631240870945$$
$$x_{32} = 36.6519142918809$$
$$x_{36} = 38.7463093942741$$
$$x_{59} = 42.9350995990605$$
$$x_{61} = 45.0294947014537$$
$$x_{58} = 49.2182849062401$$
$$x_{31} = 51.3126800086333$$
$$x_{38} = 55.5014702134197$$
$$x_{43} = 57.5958653158129$$
$$x_{44} = 61.7846555205993$$
$$x_{6} = 63.8790506229925$$
$$x_{21} = 68.0678408277789$$
$$x_{10} = 70.162235930172$$
$$x_{26} = 74.3510261349584$$
$$x_{35} = 76.4454212373516$$
$$x_{5} = 80.634211442138$$
$$x_{16} = 82.7286065445312$$
$$x_{27} = 86.9173967493176$$
$$x_{64} = 89.0117918517108$$
$$x_{18} = 93.2005820564972$$
$$x_{8} = 95.2949771588904$$
$$x_{3} = 99.4837673636768$$
$$x_{47} = 1651.43053823704$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{28}$$
For example, let's take the point
$$x_{0} = x_{28} - \frac{1}{10}$$
=
$$-359.188760060433 + - \frac{1}{10}$$
=
$$-359.288760060433$$
substitute to the expression
$$\cos{\left(t \right)} < \frac{1}{2}$$
$$\cos{\left(t \right)} < \frac{1}{2}$$
Then
$$x < -359.188760060433$$
no execute
one of the solutions of our inequality is:
$$x > -359.188760060433 \wedge x < -225.147473507269$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -359.188760060433 \wedge x < -225.147473507269$$
$$x > -99.4837673636768 \wedge x < -95.2949771588904$$
$$x > -93.2005820564972 \wedge x < -89.0117918517108$$
$$x > -86.9173967493176 \wedge x < -82.7286065445312$$
$$x > -80.634211442138 \wedge x < -76.4454212373516$$
$$x > -74.3510261349584 \wedge x < -70.162235930172$$
$$x > -68.0678408277789 \wedge x < -63.8790506229925$$
$$x > -61.7846555205993 \wedge x < -57.5958653158129$$
$$x > -55.5014702134197 \wedge x < -51.3126800086333$$
$$x > -49.2182849062401 \wedge x < -45.0294947014537$$
$$x > -42.9350995990605 \wedge x < -38.7463093942741$$
$$x > -36.6519142918809 \wedge x < -32.4631240870945$$
$$x > -30.3687289847013 \wedge x < -26.1799387799149$$
$$x > -24.0855436775217 \wedge x < -19.8967534727354$$
$$x > -17.8023583703422 \wedge x < -13.6135681655558$$
$$x > -11.5191730631626 \wedge x < -7.33038285837618$$
$$x > -5.23598775598299 \wedge x < -1.0471975511966$$
$$x > 1.0471975511966 \wedge x < 5.23598775598299$$
$$x > 7.33038285837618 \wedge x < 11.5191730631626$$
$$x > 13.6135681655558 \wedge x < 17.8023583703422$$
$$x > 19.8967534727354 \wedge x < 24.0855436775217$$
$$x > 26.1799387799149 \wedge x < 30.3687289847013$$
$$x > 32.4631240870945 \wedge x < 36.6519142918809$$
$$x > 38.7463093942741 \wedge x < 42.9350995990605$$
$$x > 45.0294947014537 \wedge x < 49.2182849062401$$
$$x > 51.3126800086333 \wedge x < 55.5014702134197$$
$$x > 57.5958653158129 \wedge x < 61.7846555205993$$
$$x > 63.8790506229925 \wedge x < 68.0678408277789$$
$$x > 70.162235930172 \wedge x < 74.3510261349584$$
$$x > 76.4454212373516 \wedge x < 80.634211442138$$
$$x > 82.7286065445312 \wedge x < 86.9173967493176$$
$$x > 89.0117918517108 \wedge x < 93.2005820564972$$
$$x > 95.2949771588904 \wedge x < 99.4837673636768$$
$$x > 1651.43053823704$$
$$\cos{\left(t \right)} < \frac{1}{2}$$
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:
$$x_{1} = -61.7846555205993$$
$$x_{2} = 17.8023583703422$$
$$x_{3} = 99.4837673636768$$
$$x_{4} = -225.147473507269$$
$$x_{5} = 80.634211442138$$
$$x_{6} = 63.8790506229925$$
$$x_{7} = -86.9173967493176$$
$$x_{8} = 95.2949771588904$$
$$x_{9} = -45.0294947014537$$
$$x_{10} = 70.162235930172$$
$$x_{11} = -26.1799387799149$$
$$x_{12} = -99.4837673636768$$
$$x_{13} = -38.7463093942741$$
$$x_{14} = 13.6135681655558$$
$$x_{15} = 24.0855436775217$$
$$x_{16} = 82.7286065445312$$
$$x_{17} = -17.8023583703422$$
$$x_{18} = 93.2005820564972$$
$$x_{19} = -80.634211442138$$
$$x_{20} = -42.9350995990605$$
$$x_{21} = 68.0678408277789$$
$$x_{22} = -49.2182849062401$$
$$x_{23} = -13.6135681655558$$
$$x_{24} = 32.4631240870945$$
$$x_{25} = -57.5958653158129$$
$$x_{26} = 74.3510261349584$$
$$x_{27} = 86.9173967493176$$
$$x_{28} = -359.188760060433$$
$$x_{29} = -55.5014702134197$$
$$x_{30} = -68.0678408277789$$
$$x_{31} = 51.3126800086333$$
$$x_{32} = 36.6519142918809$$
$$x_{33} = 7.33038285837618$$
$$x_{34} = 19.8967534727354$$
$$x_{35} = 76.4454212373516$$
$$x_{36} = 38.7463093942741$$
$$x_{37} = -32.4631240870945$$
$$x_{38} = 55.5014702134197$$
$$x_{39} = -51.3126800086333$$
$$x_{40} = -5.23598775598299$$
$$x_{41} = 30.3687289847013$$
$$x_{42} = -19.8967534727354$$
$$x_{43} = 57.5958653158129$$
$$x_{44} = 61.7846555205993$$
$$x_{45} = 5.23598775598299$$
$$x_{46} = -11.5191730631626$$
$$x_{47} = 1651.43053823704$$
$$x_{48} = -7.33038285837618$$
$$x_{49} = -1.0471975511966$$
$$x_{50} = -30.3687289847013$$
$$x_{51} = -70.162235930172$$
$$x_{52} = -93.2005820564972$$
$$x_{53} = -24.0855436775217$$
$$x_{54} = -95.2949771588904$$
$$x_{55} = 11.5191730631626$$
$$x_{56} = -89.0117918517108$$
$$x_{57} = -63.8790506229925$$
$$x_{58} = 49.2182849062401$$
$$x_{59} = 42.9350995990605$$
$$x_{60} = -76.4454212373516$$
$$x_{61} = 45.0294947014537$$
$$x_{62} = 1.0471975511966$$
$$x_{63} = 26.1799387799149$$
$$x_{64} = 89.0117918517108$$
$$x_{65} = -36.6519142918809$$
$$x_{66} = -82.7286065445312$$
$$x_{67} = -74.3510261349584$$
$$x_{1} = -61.7846555205993$$
$$x_{2} = 17.8023583703422$$
$$x_{3} = 99.4837673636768$$
$$x_{4} = -225.147473507269$$
$$x_{5} = 80.634211442138$$
$$x_{6} = 63.8790506229925$$
$$x_{7} = -86.9173967493176$$
$$x_{8} = 95.2949771588904$$
$$x_{9} = -45.0294947014537$$
$$x_{10} = 70.162235930172$$
$$x_{11} = -26.1799387799149$$
$$x_{12} = -99.4837673636768$$
$$x_{13} = -38.7463093942741$$
$$x_{14} = 13.6135681655558$$
$$x_{15} = 24.0855436775217$$
$$x_{16} = 82.7286065445312$$
$$x_{17} = -17.8023583703422$$
$$x_{18} = 93.2005820564972$$
$$x_{19} = -80.634211442138$$
$$x_{20} = -42.9350995990605$$
$$x_{21} = 68.0678408277789$$
$$x_{22} = -49.2182849062401$$
$$x_{23} = -13.6135681655558$$
$$x_{24} = 32.4631240870945$$
$$x_{25} = -57.5958653158129$$
$$x_{26} = 74.3510261349584$$
$$x_{27} = 86.9173967493176$$
$$x_{28} = -359.188760060433$$
$$x_{29} = -55.5014702134197$$
$$x_{30} = -68.0678408277789$$
$$x_{31} = 51.3126800086333$$
$$x_{32} = 36.6519142918809$$
$$x_{33} = 7.33038285837618$$
$$x_{34} = 19.8967534727354$$
$$x_{35} = 76.4454212373516$$
$$x_{36} = 38.7463093942741$$
$$x_{37} = -32.4631240870945$$
$$x_{38} = 55.5014702134197$$
$$x_{39} = -51.3126800086333$$
$$x_{40} = -5.23598775598299$$
$$x_{41} = 30.3687289847013$$
$$x_{42} = -19.8967534727354$$
$$x_{43} = 57.5958653158129$$
$$x_{44} = 61.7846555205993$$
$$x_{45} = 5.23598775598299$$
$$x_{46} = -11.5191730631626$$
$$x_{47} = 1651.43053823704$$
$$x_{48} = -7.33038285837618$$
$$x_{49} = -1.0471975511966$$
$$x_{50} = -30.3687289847013$$
$$x_{51} = -70.162235930172$$
$$x_{52} = -93.2005820564972$$
$$x_{53} = -24.0855436775217$$
$$x_{54} = -95.2949771588904$$
$$x_{55} = 11.5191730631626$$
$$x_{56} = -89.0117918517108$$
$$x_{57} = -63.8790506229925$$
$$x_{58} = 49.2182849062401$$
$$x_{59} = 42.9350995990605$$
$$x_{60} = -76.4454212373516$$
$$x_{61} = 45.0294947014537$$
$$x_{62} = 1.0471975511966$$
$$x_{63} = 26.1799387799149$$
$$x_{64} = 89.0117918517108$$
$$x_{65} = -36.6519142918809$$
$$x_{66} = -82.7286065445312$$
$$x_{67} = -74.3510261349584$$
This roots
$$x_{28} = -359.188760060433$$
$$x_{4} = -225.147473507269$$
$$x_{12} = -99.4837673636768$$
$$x_{54} = -95.2949771588904$$
$$x_{52} = -93.2005820564972$$
$$x_{56} = -89.0117918517108$$
$$x_{7} = -86.9173967493176$$
$$x_{66} = -82.7286065445312$$
$$x_{19} = -80.634211442138$$
$$x_{60} = -76.4454212373516$$
$$x_{67} = -74.3510261349584$$
$$x_{51} = -70.162235930172$$
$$x_{30} = -68.0678408277789$$
$$x_{57} = -63.8790506229925$$
$$x_{1} = -61.7846555205993$$
$$x_{25} = -57.5958653158129$$
$$x_{29} = -55.5014702134197$$
$$x_{39} = -51.3126800086333$$
$$x_{22} = -49.2182849062401$$
$$x_{9} = -45.0294947014537$$
$$x_{20} = -42.9350995990605$$
$$x_{13} = -38.7463093942741$$
$$x_{65} = -36.6519142918809$$
$$x_{37} = -32.4631240870945$$
$$x_{50} = -30.3687289847013$$
$$x_{11} = -26.1799387799149$$
$$x_{53} = -24.0855436775217$$
$$x_{42} = -19.8967534727354$$
$$x_{17} = -17.8023583703422$$
$$x_{23} = -13.6135681655558$$
$$x_{46} = -11.5191730631626$$
$$x_{48} = -7.33038285837618$$
$$x_{40} = -5.23598775598299$$
$$x_{49} = -1.0471975511966$$
$$x_{62} = 1.0471975511966$$
$$x_{45} = 5.23598775598299$$
$$x_{33} = 7.33038285837618$$
$$x_{55} = 11.5191730631626$$
$$x_{14} = 13.6135681655558$$
$$x_{2} = 17.8023583703422$$
$$x_{34} = 19.8967534727354$$
$$x_{15} = 24.0855436775217$$
$$x_{63} = 26.1799387799149$$
$$x_{41} = 30.3687289847013$$
$$x_{24} = 32.4631240870945$$
$$x_{32} = 36.6519142918809$$
$$x_{36} = 38.7463093942741$$
$$x_{59} = 42.9350995990605$$
$$x_{61} = 45.0294947014537$$
$$x_{58} = 49.2182849062401$$
$$x_{31} = 51.3126800086333$$
$$x_{38} = 55.5014702134197$$
$$x_{43} = 57.5958653158129$$
$$x_{44} = 61.7846555205993$$
$$x_{6} = 63.8790506229925$$
$$x_{21} = 68.0678408277789$$
$$x_{10} = 70.162235930172$$
$$x_{26} = 74.3510261349584$$
$$x_{35} = 76.4454212373516$$
$$x_{5} = 80.634211442138$$
$$x_{16} = 82.7286065445312$$
$$x_{27} = 86.9173967493176$$
$$x_{64} = 89.0117918517108$$
$$x_{18} = 93.2005820564972$$
$$x_{8} = 95.2949771588904$$
$$x_{3} = 99.4837673636768$$
$$x_{47} = 1651.43053823704$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{28}$$
For example, let's take the point
$$x_{0} = x_{28} - \frac{1}{10}$$
=
$$-359.188760060433 + - \frac{1}{10}$$
=
$$-359.288760060433$$
substitute to the expression
$$\cos{\left(t \right)} < \frac{1}{2}$$
$$\cos{\left(t \right)} < \frac{1}{2}$$
cos(t) < 1/2
Then
$$x < -359.188760060433$$
no execute
one of the solutions of our inequality is:
$$x > -359.188760060433 \wedge x < -225.147473507269$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------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-------
x28 x4 x12 x54 x52 x56 x7 x66 x19 x60 x67 x51 x30 x57 x1 x25 x29 x39 x22 x9 x20 x13 x65 x37 x50 x11 x53 x42 x17 x23 x46 x48 x40 x49 x62 x45 x33 x55 x14 x2 x34 x15 x63 x41 x24 x32 x36 x59 x61 x58 x31 x38 x43 x44 x6 x21 x10 x26 x35 x5 x16 x27 x64 x18 x8 x3 x47Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -359.188760060433 \wedge x < -225.147473507269$$
$$x > -99.4837673636768 \wedge x < -95.2949771588904$$
$$x > -93.2005820564972 \wedge x < -89.0117918517108$$
$$x > -86.9173967493176 \wedge x < -82.7286065445312$$
$$x > -80.634211442138 \wedge x < -76.4454212373516$$
$$x > -74.3510261349584 \wedge x < -70.162235930172$$
$$x > -68.0678408277789 \wedge x < -63.8790506229925$$
$$x > -61.7846555205993 \wedge x < -57.5958653158129$$
$$x > -55.5014702134197 \wedge x < -51.3126800086333$$
$$x > -49.2182849062401 \wedge x < -45.0294947014537$$
$$x > -42.9350995990605 \wedge x < -38.7463093942741$$
$$x > -36.6519142918809 \wedge x < -32.4631240870945$$
$$x > -30.3687289847013 \wedge x < -26.1799387799149$$
$$x > -24.0855436775217 \wedge x < -19.8967534727354$$
$$x > -17.8023583703422 \wedge x < -13.6135681655558$$
$$x > -11.5191730631626 \wedge x < -7.33038285837618$$
$$x > -5.23598775598299 \wedge x < -1.0471975511966$$
$$x > 1.0471975511966 \wedge x < 5.23598775598299$$
$$x > 7.33038285837618 \wedge x < 11.5191730631626$$
$$x > 13.6135681655558 \wedge x < 17.8023583703422$$
$$x > 19.8967534727354 \wedge x < 24.0855436775217$$
$$x > 26.1799387799149 \wedge x < 30.3687289847013$$
$$x > 32.4631240870945 \wedge x < 36.6519142918809$$
$$x > 38.7463093942741 \wedge x < 42.9350995990605$$
$$x > 45.0294947014537 \wedge x < 49.2182849062401$$
$$x > 51.3126800086333 \wedge x < 55.5014702134197$$
$$x > 57.5958653158129 \wedge x < 61.7846555205993$$
$$x > 63.8790506229925 \wedge x < 68.0678408277789$$
$$x > 70.162235930172 \wedge x < 74.3510261349584$$
$$x > 76.4454212373516 \wedge x < 80.634211442138$$
$$x > 82.7286065445312 \wedge x < 86.9173967493176$$
$$x > 89.0117918517108 \wedge x < 93.2005820564972$$
$$x > 95.2949771588904 \wedge x < 99.4837673636768$$
$$x > 1651.43053823704$$
Rapid solution
[src]
/pi 5*pi\ And|-- < t, t < ----| \3 3 /
$$\frac{\pi}{3} < t \wedge t < \frac{5 \pi}{3}$$
(pi/3 < t)∧(t < 5*pi/3)
Rapid solution 2
[src]
pi 5*pi (--, ----) 3 3
$$x\ in\ \left(\frac{\pi}{3}, \frac{5 \pi}{3}\right)$$
x in Interval.open(pi/3, 5*pi/3)