^{1/2})sinx+cosx

(3^{1/2})sinx+cosx

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To find the maximum, I would use calculus. if you don't know calculus, then you should graph this on a graphing calculator or using graph paper & find the highest point on the graph.

Using calculus:

y = 3^.5 * sin x + cos x

y' = 3^.5 * cos x - sin x

3^.5 * cos x - sin x = 0

3^.5 * cos x = sin x

3^.5 = tan x

x = pi/3 & 4pi/3

When pi/3 is put into the original equation, the answer is positive. However, the answer is negative when 4pi/3 is put in. The maximum would have to be at pi/3

y = 3^.5 * sin (pi/3) + cos (pi/3) = (3^.5)(3^.5)/2 + 1/2 = 3/2 + 1/2 = 2

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