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$$\cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)} = 0$$
Solve this equationThe roots of this equation
$$x_{1} = 7.85398163397448$$
$$x_{2} = -73.8274273593601$$
$$x_{3} = -54.9778714378214$$
$$x_{4} = 73.8274273593601$$
$$x_{5} = 0$$
$$x_{6} = -26.7035375555132$$
$$x_{7} = -1.5707963267949$$
$$x_{8} = -306.305283725005$$
$$x_{9} = -95.8185759344887$$
$$x_{10} = -39.2699081698724$$
$$x_{11} = -4.71238898038469$$
$$x_{12} = 14.1371669411541$$
$$x_{13} = 10.9955742875643$$
$$x_{14} = 58.1194640914112$$
$$x_{15} = 70.6858347057703$$
$$x_{16} = -36.1283155162826$$
$$x_{17} = 54.9778714378214$$
$$x_{18} = 23.5619449019235$$
$$x_{19} = 237.190245346029$$
$$x_{20} = -92.6769832808989$$
$$x_{21} = -86.3937979737193$$
$$x_{22} = -10.9955742875643$$
$$x_{23} = 92.6769832808989$$
$$x_{24} = 39.2699081698724$$
$$x_{25} = -32.9867228626928$$
$$x_{26} = 98.9601685880785$$
$$x_{27} = 36.1283155162826$$
$$x_{28} = -7.85398163397448$$
$$x_{29} = -58.1194640914112$$
$$x_{30} = -67.5442420521806$$
$$x_{31} = -61.261056745001$$
$$x_{32} = 26.7035375555132$$
$$x_{33} = 86.3937979737193$$
$$x_{34} = -48.6946861306418$$
$$x_{35} = 51.8362787842316$$
$$x_{36} = -42.4115008234622$$
$$x_{37} = -89.5353906273091$$
$$x_{38} = -98.9601685880785$$
$$x_{39} = -14.1371669411541$$
$$x_{40} = 80.1106126665397$$
$$x_{41} = -64.4026493985908$$
$$x_{42} = 95.8185759344887$$
$$x_{43} = 1.5707963267949$$
$$x_{44} = 45.553093477052$$
$$x_{45} = -17.2787595947439$$
$$x_{46} = 4.71238898038469$$
$$x_{47} = 48.6946861306418$$
$$x_{48} = 76.9690200129499$$
$$x_{49} = -45.553093477052$$
$$x_{50} = -183.783170235003$$
$$x_{51} = 20.4203522483337$$
$$x_{52} = 17.2787595947439$$
$$x_{53} = -83.2522053201295$$
$$x_{54} = -20.4203522483337$$
$$x_{55} = -80.1106126665397$$
$$x_{56} = 61.261056745001$$
$$x_{57} = 32.9867228626928$$
$$x_{58} = 64.4026493985908$$
$$x_{59} = -23.5619449019235$$
$$x_{60} = 29.845130209103$$
$$x_{61} = 42.4115008234622$$
$$x_{62} = 89.5353906273091$$
$$x_{63} = -51.8362787842316$$
$$x_{64} = -70.6858347057703$$
$$x_{65} = 83.2522053201295$$
$$x_{66} = 67.5442420521806$$
$$x_{67} = -29.845130209103$$
$$x_{68} = -76.9690200129499$$
$$x_{69} = -2279.22547017939$$
The values of the extrema at the points:
(7.853981633974483, 1)
(-73.82742735936014, 1)
(-54.977871437821385, 1)
(73.82742735936014, 1)
(0, 0)
(-26.703537555513243, 1)
(-1.5707963267948966, 1)
(-306.3052837250048, 1)
(-95.81857593448869, 1)
(-39.269908169872416, 1)
(-4.71238898038469, 1)
(14.137166941154069, 1)
(10.995574287564276, 1)
(58.119464091411174, 1)
(70.68583470577035, 1)
(-36.12831551628262, 1)
(54.977871437821385, 1)
(23.56194490192345, 1)
(237.1902453460294, 1)
(-92.6769832808989, 1)
(-86.39379797371932, 1)
(-10.995574287564276, 1)
(92.6769832808989, 1)
(39.269908169872416, 1)
(-32.98672286269283, 1)
(98.96016858807849, 1)
(36.12831551628262, 1)
(-7.853981633974483, 1)
(-58.119464091411174, 1)
(-67.54424205218055, 1)
(-61.26105674500097, 1)
(26.703537555513243, 1)
(86.39379797371932, 1)
(-48.6946861306418, 1)
(51.83627878423159, 1)
(-42.411500823462205, 1)
(-89.53539062730911, 1)
(-98.96016858807849, 1)
(-14.137166941154069, 1)
(80.11061266653972, 1)
(-64.40264939859077, 1)
(95.81857593448869, 1)
(1.5707963267948966, 1)
(45.553093477052, 1)
(-17.278759594743864, 1)
(4.71238898038469, 1)
(48.6946861306418, 1)
(76.96902001294994, 1)
(-45.553093477052, 1)
(-183.7831702350029, 1)
(20.420352248333657, 1)
(17.278759594743864, 1)
(-83.25220532012952, 1)
(-20.420352248333657, 1)
(-80.11061266653972, 1)
(61.26105674500097, 1)
(32.98672286269283, 1)
(64.40264939859077, 1)
(-23.56194490192345, 1)
(29.845130209103036, 1)
(42.411500823462205, 1)
(89.53539062730911, 1)
(-51.83627878423159, 1)
(-70.68583470577035, 1)
(83.25220532012952, 1)
(67.54424205218055, 1)
(-29.845130209103036, 1)
(-76.96902001294994, 1)
(-2279.225470179395, 1)
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:
Minima of the function at points:
$$x_{1} = 0$$
Maxima of the function at points:
$$x_{1} = 7.85398163397448$$
$$x_{1} = -73.8274273593601$$
$$x_{1} = -54.9778714378214$$
$$x_{1} = 73.8274273593601$$
$$x_{1} = -26.7035375555132$$
$$x_{1} = -1.5707963267949$$
$$x_{1} = -306.305283725005$$
$$x_{1} = -95.8185759344887$$
$$x_{1} = -39.2699081698724$$
$$x_{1} = -4.71238898038469$$
$$x_{1} = 14.1371669411541$$
$$x_{1} = 10.9955742875643$$
$$x_{1} = 58.1194640914112$$
$$x_{1} = 70.6858347057703$$
$$x_{1} = -36.1283155162826$$
$$x_{1} = 54.9778714378214$$
$$x_{1} = 23.5619449019235$$
$$x_{1} = 237.190245346029$$
$$x_{1} = -92.6769832808989$$
$$x_{1} = -86.3937979737193$$
$$x_{1} = -10.9955742875643$$
$$x_{1} = 92.6769832808989$$
$$x_{1} = 39.2699081698724$$
$$x_{1} = -32.9867228626928$$
$$x_{1} = 98.9601685880785$$
$$x_{1} = 36.1283155162826$$
$$x_{1} = -7.85398163397448$$
$$x_{1} = -58.1194640914112$$
$$x_{1} = -67.5442420521806$$
$$x_{1} = -61.261056745001$$
$$x_{1} = 26.7035375555132$$
$$x_{1} = 86.3937979737193$$
$$x_{1} = -48.6946861306418$$
$$x_{1} = 51.8362787842316$$
$$x_{1} = -42.4115008234622$$
$$x_{1} = -89.5353906273091$$
$$x_{1} = -98.9601685880785$$
$$x_{1} = -14.1371669411541$$
$$x_{1} = 80.1106126665397$$
$$x_{1} = -64.4026493985908$$
$$x_{1} = 95.8185759344887$$
$$x_{1} = 1.5707963267949$$
$$x_{1} = 45.553093477052$$
$$x_{1} = -17.2787595947439$$
$$x_{1} = 4.71238898038469$$
$$x_{1} = 48.6946861306418$$
$$x_{1} = 76.9690200129499$$
$$x_{1} = -45.553093477052$$
$$x_{1} = -183.783170235003$$
$$x_{1} = 20.4203522483337$$
$$x_{1} = 17.2787595947439$$
$$x_{1} = -83.2522053201295$$
$$x_{1} = -20.4203522483337$$
$$x_{1} = -80.1106126665397$$
$$x_{1} = 61.261056745001$$
$$x_{1} = 32.9867228626928$$
$$x_{1} = 64.4026493985908$$
$$x_{1} = -23.5619449019235$$
$$x_{1} = 29.845130209103$$
$$x_{1} = 42.4115008234622$$
$$x_{1} = 89.5353906273091$$
$$x_{1} = -51.8362787842316$$
$$x_{1} = -70.6858347057703$$
$$x_{1} = 83.2522053201295$$
$$x_{1} = 67.5442420521806$$
$$x_{1} = -29.845130209103$$
$$x_{1} = -76.9690200129499$$
$$x_{1} = -2279.22547017939$$
Decreasing at intervals
$$\left(-\infty, -2279.22547017939\right] \cup \left[0, \infty\right)$$
Increasing at intervals
$$\left(-\infty, 0\right] \cup \left[237.190245346029, \infty\right)$$