Question Number 122843 by ZiYangLee last updated on 20/Nov/20
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{y}=\mathrm{cos}^{\mathrm{2}} {x}−\mathrm{3cos}\:{x}+\mathrm{5} \\ $$
Commented by Dwaipayan Shikari last updated on 20/Nov/20
$$−\mathrm{1}\leqslant{cosx}\leqslant\mathrm{1} \\ $$$$−\mathrm{3}\leqslant−\mathrm{3}{cosx}\leqslant\mathrm{3}\:\:\:\:\:\:\:\:\:\: \\ $$$${Range}\:\:\:{y}_{{min}} =−\mathrm{3}+\mathrm{5}+\mathrm{1}=\mathrm{3} \\ $$$${y}_{{max}} =\:\mathrm{3}+\mathrm{5}+\mathrm{1}=\mathrm{9} \\ $$$$\mathrm{3}\leqslant{y}\leqslant\mathrm{9} \\ $$
Commented by ZiYangLee last updated on 21/Nov/20
$$\mathrm{thanks} \\ $$