How do you graph #f(x)=2cosx-(sqrt2)# and solve over the interval [0,2pi)?

1 Answer
Feb 13, 2015

The graph of #f(x) = 2 cos(x) - ( sqrt(2) )#
is simply the graph of #2 cos(x)# shifted down by #( sqrt(2) )#
(where #2 cos(x)# is simply #cos(x)# stretched vertically by a factor of #2#).
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I was not certain what you meant by "solve"; I have assumed you meant:
solve for #x# when # 2 cos(x) - ( sqrt(2) ) = 0#

#2 cos(x) - sqrt(2) = 0#

#2 cos(x) = sqrt(2)#

#cos(x) = ( 1 / sqrt(2) )#

(This is a standard #45^o angle)

Within the specified range #f(x) = 0#
when
#x = 45^o# (#Pi/4# radians)
and
#x = 315^o# (#(7Pi)/4# radians)