The max value of #5cosα+3cos(α+π/3)+3 # is?

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Answer 1 · 2018-08-04T15:55:14

10
See graphical depiction.

#5 cos alpha + 3 cos ( alpha + pi/3 ) +3#

#= 5 cos alpha + 3 ( cos alpha cos (pi/3) - sin alpha sin (pi/3) ) + 3#

#= 13/2 cos alpha - 3/2 sqrt 3 sin alpha + 3#

#= sqrt( (13/2)^2+ (3/2sqrt3)^2) (cos alpha cos beta - sin alpha

sin beta ) + 3#

#= 7 cos ( alpha + beta ) + 3, beta = arccos (13/14)#

As cosine value #in [ - 1, 1 ]#, the maximum of the given function

#= max 7 [ - 1, 1 ] + 3 = 7 + 3 = 10#

graph{(5 cos x + 3 cos ( x + pi/3 ) +3 - y )(y-10+0x)= 0[-10 10 0 10.2]}