Given-that-y-3-sin-x-4-cos-x-6-2-0-x-2pi-Find-the-smallest-value-of-y-

Question Number 160605 by ZiYangLee last updated on 03/Dec/21

Given that y = {(3 \sin x - 4 \cos x + 6)}^{2}, 0 ⩽ x ⩽ 2 π .

Find the smallest value of y .

Commented by cortano last updated on 03/Dec/21

y = {[5 (\frac{3}{5} \sin x - \frac{4}{5} \cos x) + 6]}^{2}

y = {[5 \sin (α - x) + 6]}^{2}; α = \cos^{- 1} (\frac{3}{5})

y_{\max} = 121

y_{\min} = 1

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