El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\cos{\left(\frac{x + \pi}{4} \right)} - 1 = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución analítica$$x_{1} = - \pi$$
$$x_{2} = 7 \pi$$
Solución numérica$$x_{1} = -3.14159383006953$$
$$x_{2} = 72.2566318788299$$
$$x_{3} = -78.5398177408664$$
$$x_{4} = -28.2743324282563$$
$$x_{5} = 21.9911469952148$$
$$x_{6} = -28.274338935394$$
$$x_{7} = -28.2743321275734$$
$$x_{8} = 21.991154189523$$
$$x_{9} = 21.9911448073251$$
$$x_{10} = -103.672559322976$$
$$x_{11} = -53.4070765037245$$
$$x_{12} = 21.9911467826204$$
$$x_{13} = -3.14159066703545$$
$$x_{14} = 72.256633066684$$
$$x_{15} = 47.1238890960547$$
$$x_{16} = -28.2743318189218$$
$$x_{17} = 47.1238879198977$$
$$x_{18} = 8139.86656510072$$
$$x_{19} = -28.2743353753204$$
$$x_{20} = 72.2566310277172$$
$$x_{21} = 72.2566289094197$$
$$x_{22} = 47.1238893682042$$
$$x_{23} = 72.2566326324851$$
$$x_{24} = -3.14159375810549$$
$$x_{25} = -3.14159296681419$$
$$x_{26} = 97.389370885462$$
$$x_{27} = 97.3893721068933$$
$$x_{28} = -78.5398142810183$$
$$x_{29} = 72.2566347868398$$
$$x_{30} = 21.9911506864752$$
$$x_{31} = 21.9911495333853$$
$$x_{32} = -103.672555541645$$
$$x_{33} = -3.14159250467346$$
$$x_{34} = 47.123888525652$$
$$x_{35} = -3.14159447715332$$
$$x_{36} = -3.14159070339079$$
$$x_{37} = -28.2743345873237$$
$$x_{38} = -78.5398151668605$$
$$x_{39} = -28.2743358735612$$
$$x_{40} = -53.4070752984459$$
$$x_{41} = -78.5398151517367$$
$$x_{42} = -128.805305003568$$
$$x_{43} = 72.2566300998441$$
$$x_{44} = 47.1238902666794$$
$$x_{45} = -53.4070771673643$$
$$x_{46} = 97.3893734617364$$
$$x_{47} = -757.123834111091$$
$$x_{48} = -3.14159207076295$$
$$x_{49} = -78.5398163114628$$
$$x_{50} = -53.4070736207379$$
$$x_{51} = -103.672555990926$$
$$x_{52} = -53.4070761820751$$
$$x_{53} = -53.4070731912959$$
$$x_{54} = -53.4070744104623$$
$$x_{55} = 47.1238905077539$$
$$x_{56} = 21.9911477549563$$
$$x_{57} = 47.1238917026787$$
$$x_{58} = -53.4070757473989$$
$$x_{59} = 21.9911502245891$$
$$x_{60} = 72.2566289869004$$
$$x_{61} = -3.14159470276401$$
$$x_{62} = -706.858345905212$$
$$x_{63} = -3647.38907316924$$
$$x_{64} = 21.9911485852088$$
$$x_{65} = 47.1238918341433$$
$$x_{66} = 97.3893726016239$$
$$x_{67} = -53.407076867141$$
$$x_{68} = -78.5398182890653$$
$$x_{69} = 21.9911465514132$$
$$x_{70} = -28.2743328150664$$
$$x_{71} = -3.14159125549584$$
$$x_{72} = -28.2743357780456$$
$$x_{73} = -78.5398145169975$$
$$x_{74} = -78.5398160326333$$
$$x_{75} = 21.9911506297789$$
$$x_{76} = -53.4070731178921$$
$$x_{77} = 21.9911502554244$$
$$x_{78} = -28.2743337039516$$
$$x_{79} = -103.672555744213$$
$$x_{80} = 47.1238911052008$$
$$x_{81} = 72.2566293711688$$
$$x_{82} = 97.3893717054584$$
$$x_{83} = 47.1238877779901$$
$$x_{84} = -53.4070705230011$$
$$x_{85} = 97.3893702778698$$
$$x_{86} = 97.3893703246335$$
$$x_{87} = 72.2566293825787$$
$$x_{88} = -78.5398183081238$$
$$x_{89} = -28.2743329935772$$
$$x_{90} = 72.2566328255686$$
$$x_{91} = -78.5398169272729$$