Question Number 81008 by M±th+et£s last updated on 08/Feb/20
Commented by jagoll last updated on 09/Feb/20
$$\left(\mathrm{2}\right){a}\mathrm{sin}\:{t}\:+\:{b}\mathrm{cos}\:{t}\:=\:\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }\:\mathrm{cos}\:\left({t}−\alpha\right) \\ $$$${where}\:\alpha\:=\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{{a}}{{b}}\right) \\ $$$${max}\:{value}\:=\:\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} } \\ $$$${min}\:{value}\:=\:−\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} } \\ $$