We know that #sin# and #cos# has a period of #2pi#. That is to say that it repeats itself every #2pi# units.
I would assume you know how to graph a #f(x)=cos(x)# functions, if not, it should look like this:
Now, you need to graph #f(x)=cos(x+pi/6)#.
Imagine you have a function #f(x)# and another function #g(x)=f(x+1)#.
What this means is that for any point #(x, y)# on the graph #g(x)#, it will take #x+1# units for #f(x)# to reach that same #y# value.
That is what this #g(x)=f(x+1)# is saying.
This means that all points on #g(x)# is occurring 1 unit earlier than #f(x)# so we shift #f(x)# to the left by 1 unit to obtain #g(x)#.
To generalize:
If #g(x)=f(x+n)# we shift #f(x) #n# units to the **left** to get #g(x)#.
If #g(x)=f(x-n)# we shift #f(x) #n# units to the right to get #g(x)#.
Now, we can apply it to this question:
We have #f(x)=cos(x+pi/6)# which is basically saying we should shift #cos(x)# to the left by #pi/6# units.
The blue curve is your #y=cos(x+pi/6)#
The red curve is your #y=cos(x)#
