In order to find the extrema, we need to solve the equation
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d x} f{\left(x \right)} = $$
the first derivative$$\frac{12 \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{12 \sin{\left(x \right)}}\right|} = 0$$
Solve this equationThe roots of this equation
$$x_{1} = 48.6946861306418$$
$$x_{2} = -54.9778714378214$$
$$x_{3} = 92.6769832808989$$
$$x_{4} = 10.9955742875643$$
$$x_{5} = 7.85398163397448$$
$$x_{6} = 1.5707963267949$$
$$x_{7} = -58.1194640914112$$
$$x_{8} = -67.5442420521806$$
$$x_{9} = 26.7035375555132$$
$$x_{10} = -45.553093477052$$
$$x_{11} = -36.1283155162826$$
$$x_{12} = -4.71238898038469$$
$$x_{13} = 64.4026493985908$$
$$x_{14} = -95.8185759344887$$
$$x_{15} = -7.85398163397448$$
$$x_{16} = -20.4203522483337$$
$$x_{17} = 45.553093477052$$
$$x_{18} = 89.5353906273091$$
$$x_{19} = 73.8274273593601$$
$$x_{20} = 61.261056745001$$
$$x_{21} = -76.9690200129499$$
$$x_{22} = 70.6858347057703$$
$$x_{23} = -89.5353906273091$$
$$x_{24} = 67.5442420521806$$
$$x_{25} = -48.6946861306418$$
$$x_{26} = 4.71238898038469$$
$$x_{27} = 36.1283155162826$$
$$x_{28} = -70.6858347057703$$
$$x_{29} = -42.4115008234622$$
$$x_{30} = 76.9690200129499$$
$$x_{31} = -51.8362787842316$$
$$x_{32} = -39.2699081698724$$
$$x_{33} = 54.9778714378214$$
$$x_{34} = -80.1106126665397$$
$$x_{35} = -64.4026493985908$$
$$x_{36} = 42.4115008234622$$
$$x_{37} = -10.9955742875643$$
$$x_{38} = 39.2699081698724$$
$$x_{39} = -61.261056745001$$
$$x_{40} = 20.4203522483337$$
$$x_{41} = 58.1194640914112$$
$$x_{42} = -14.1371669411541$$
$$x_{43} = 51.8362787842316$$
$$x_{44} = 95.8185759344887$$
$$x_{45} = 32.9867228626928$$
$$x_{46} = 98.9601685880785$$
$$x_{47} = -26.7035375555132$$
$$x_{48} = 29.845130209103$$
$$x_{49} = -29.845130209103$$
$$x_{50} = -86.3937979737193$$
$$x_{51} = -32.9867228626928$$
$$x_{52} = 80.1106126665397$$
$$x_{53} = -83.2522053201295$$
$$x_{54} = 86.3937979737193$$
$$x_{55} = 23.5619449019235$$
$$x_{56} = -1.5707963267949$$
$$x_{57} = -17.2787595947439$$
$$x_{58} = 14.1371669411541$$
$$x_{59} = -98.9601685880785$$
$$x_{60} = -23.5619449019235$$
$$x_{61} = -73.8274273593601$$
$$x_{62} = 17.2787595947439$$
$$x_{63} = 83.2522053201295$$
$$x_{64} = -92.6769832808989$$
The values of the extrema at the points:
(48.6946861306418, 2.484906649788)
(-54.9778714378214, 2.484906649788)
(92.6769832808989, 2.484906649788)
(10.9955742875643, 2.484906649788)
(7.85398163397448, 2.484906649788)
(1.5707963267949, 2.484906649788)
(-58.1194640914112, 2.484906649788)
(-67.5442420521806, 2.484906649788)
(26.7035375555132, 2.484906649788)
(-45.553093477052, 2.484906649788)
(-36.1283155162826, 2.484906649788)
(-4.71238898038469, 2.484906649788)
(64.4026493985908, 2.484906649788)
(-95.8185759344887, 2.484906649788)
(-7.85398163397448, 2.484906649788)
(-20.4203522483337, 2.484906649788)
(45.553093477052, 2.484906649788)
(89.5353906273091, 2.484906649788)
(73.8274273593601, 2.484906649788)
(61.261056745001, 2.484906649788)
(-76.9690200129499, 2.484906649788)
(70.6858347057703, 2.484906649788)
(-89.5353906273091, 2.484906649788)
(67.5442420521806, 2.484906649788)
(-48.6946861306418, 2.484906649788)
(4.71238898038469, 2.484906649788)
(36.1283155162826, 2.484906649788)
(-70.6858347057703, 2.484906649788)
(-42.4115008234622, 2.484906649788)
(76.9690200129499, 2.484906649788)
(-51.8362787842316, 2.484906649788)
(-39.2699081698724, 2.484906649788)
(54.9778714378214, 2.484906649788)
(-80.1106126665397, 2.484906649788)
(-64.4026493985908, 2.484906649788)
(42.4115008234622, 2.484906649788)
(-10.9955742875643, 2.484906649788)
(39.2699081698724, 2.484906649788)
(-61.261056745001, 2.484906649788)
(20.4203522483337, 2.484906649788)
(58.1194640914112, 2.484906649788)
(-14.1371669411541, 2.484906649788)
(51.8362787842316, 2.484906649788)
(95.8185759344887, 2.484906649788)
(32.9867228626928, 2.484906649788)
(98.9601685880785, 2.484906649788)
(-26.7035375555132, 2.484906649788)
(29.845130209103, 2.484906649788)
(-29.845130209103, 2.484906649788)
(-86.3937979737193, 2.484906649788)
(-32.9867228626928, 2.484906649788)
(80.1106126665397, 2.484906649788)
(-83.2522053201295, 2.484906649788)
(86.3937979737193, 2.484906649788)
(23.5619449019235, 2.484906649788)
(-1.5707963267949, 2.484906649788)
(-17.2787595947439, 2.484906649788)
(14.1371669411541, 2.484906649788)
(-98.9601685880785, 2.484906649788)
(-23.5619449019235, 2.484906649788)
(-73.8274273593601, 2.484906649788)
(17.2787595947439, 2.484906649788)
(83.2522053201295, 2.484906649788)
(-92.6769832808989, 2.484906649788)
Intervals of increase and decrease of the function:Let's find intervals where the function increases and decreases, as well as minima and maxima of the function, for this let's look how the function behaves itself in the extremas and at the slightest deviation from:
The function has no minima
Maxima of the function at points:
$$x_{64} = 48.6946861306418$$
$$x_{64} = -54.9778714378214$$
$$x_{64} = 92.6769832808989$$
$$x_{64} = 10.9955742875643$$
$$x_{64} = 7.85398163397448$$
$$x_{64} = 1.5707963267949$$
$$x_{64} = -58.1194640914112$$
$$x_{64} = -67.5442420521806$$
$$x_{64} = 26.7035375555132$$
$$x_{64} = -45.553093477052$$
$$x_{64} = -36.1283155162826$$
$$x_{64} = -4.71238898038469$$
$$x_{64} = 64.4026493985908$$
$$x_{64} = -95.8185759344887$$
$$x_{64} = -7.85398163397448$$
$$x_{64} = -20.4203522483337$$
$$x_{64} = 45.553093477052$$
$$x_{64} = 89.5353906273091$$
$$x_{64} = 73.8274273593601$$
$$x_{64} = 61.261056745001$$
$$x_{64} = -76.9690200129499$$
$$x_{64} = 70.6858347057703$$
$$x_{64} = -89.5353906273091$$
$$x_{64} = 67.5442420521806$$
$$x_{64} = -48.6946861306418$$
$$x_{64} = 4.71238898038469$$
$$x_{64} = 36.1283155162826$$
$$x_{64} = -70.6858347057703$$
$$x_{64} = -42.4115008234622$$
$$x_{64} = 76.9690200129499$$
$$x_{64} = -51.8362787842316$$
$$x_{64} = -39.2699081698724$$
$$x_{64} = 54.9778714378214$$
$$x_{64} = -80.1106126665397$$
$$x_{64} = -64.4026493985908$$
$$x_{64} = 42.4115008234622$$
$$x_{64} = -10.9955742875643$$
$$x_{64} = 39.2699081698724$$
$$x_{64} = -61.261056745001$$
$$x_{64} = 20.4203522483337$$
$$x_{64} = 58.1194640914112$$
$$x_{64} = -14.1371669411541$$
$$x_{64} = 51.8362787842316$$
$$x_{64} = 95.8185759344887$$
$$x_{64} = 32.9867228626928$$
$$x_{64} = 98.9601685880785$$
$$x_{64} = -26.7035375555132$$
$$x_{64} = 29.845130209103$$
$$x_{64} = -29.845130209103$$
$$x_{64} = -86.3937979737193$$
$$x_{64} = -32.9867228626928$$
$$x_{64} = 80.1106126665397$$
$$x_{64} = -83.2522053201295$$
$$x_{64} = 86.3937979737193$$
$$x_{64} = 23.5619449019235$$
$$x_{64} = -1.5707963267949$$
$$x_{64} = -17.2787595947439$$
$$x_{64} = 14.1371669411541$$
$$x_{64} = -98.9601685880785$$
$$x_{64} = -23.5619449019235$$
$$x_{64} = -73.8274273593601$$
$$x_{64} = 17.2787595947439$$
$$x_{64} = 83.2522053201295$$
$$x_{64} = -92.6769832808989$$
Decreasing at intervals
$$\left(-\infty, -98.9601685880785\right]$$
Increasing at intervals
$$\left[98.9601685880785, \infty\right)$$