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find the maximum value of:

5+sinx-3cosx and state the value of x for which this maximum occurs

y = 5 + sin x - 3 cos x

dy/dx = 0 at min or max = cos x + 3 sin x

cos x = - 3 sin x

tan x = -1/3

x = -18.4 deg

that is in quadrants 2 and 4

x = 161.6 and 341.6 degrees

at 161.6
5 + sin x -3 cos x =5.27
at 341.6
5 + sin x -3 cos x = 4.64
looks like at 161.6 degrees for max

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