Question Number 97656 by Vishal Sharma last updated on 09/Jun/20
$$\mathrm{Maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{3}\:\mathrm{cos}\:\theta\:+\:\mathrm{4}\:\mathrm{sin}\:\theta\:\mathrm{is} \\ $$
Commented by bobhans last updated on 09/Jun/20
$$\mathrm{max}\:=\:\mathrm{5} \\ $$$$\mathrm{min}\:=\:−\mathrm{5} \\ $$
Answered by Rio Michael last updated on 09/Jun/20
$$\mathrm{3}\:\mathrm{cos}\:\theta\:+\:\mathrm{4}\:\mathrm{sin}\:\theta\:=\:\mathrm{5}\:\mathrm{cos}\:\left({x}−\mathrm{43}°\right) \\ $$$$\mathrm{max}\:=\:\mathrm{5} \\ $$$$\mathrm{min}\:=\:−\mathrm{5} \\ $$$$\:\mathrm{as}\:\:\:−\mathrm{5}\:\leqslant\:\mathrm{5}\:\mathrm{cos}\left({x}−\mathrm{43}°\right)\:\leqslant\:\mathrm{5} \\ $$