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Find-the-range-of-y-cos-2-x-3cos-x-5-




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

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