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Question Number 81008 by M±th+et£s last updated on 08/Feb/20

Commented by jagoll last updated on 09/Feb/20

(2)asin t + bcos t = (√(a^2 +b^2 )) cos (t−α)  where α = tan^(−1) ((a/b))  max value = (√(a^2 +b^2 ))  min value = −(√(a^2 +b^2 ))

$$\left(\mathrm{2}\right){a}\mathrm{sin}\:{t}\:+\:{b}\mathrm{cos}\:{t}\:=\:\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }\:\mathrm{cos}\:\left({t}−\alpha\right) \\ $$$${where}\:\alpha\:=\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{{a}}{{b}}\right) \\ $$$${max}\:{value}\:=\:\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} } \\ $$$${min}\:{value}\:=\:−\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} } \\ $$

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