Translating Sine and Cosine Functions
Key Questions

For an equation:
A vertical translation is of the form:
#y = sin(theta) + A# where# A!=0#
OR#y = cos(theta) + A# Example:
#y = sin(theta) + 5# is a#sin# graph that has been shifted up by 5 unitsThe graph
#y = cos(theta)  1# is a graph of#cos# shifted down the yaxis by 1 unitA horizontal translation is of the form:
#y = sin(theta + A)# where#A!=0# Examples:
The graph#y = sin(theta + pi/2)# is a graph of#sin# that has been shifted#pi/2# radians to the rightFor a graph:
I'm to illustrate with an example given above:For compare:
#y = cos(theta)#
graph{cosx [5.325, 6.675, 5.16, 4.84]}and
#y = cos(theta)  1#
graph{cosx 1 [5.325, 6.675, 5.16, 4.84]}
To verify that the graph of#y = cos(theta)  1# is a vertical translation, if you look on the graph,the point where
#theta = 0# is no more at#y = 1# it is now at# y = 0# That is, the original graph of
#y= costheta# has been shifted down by 1 unit.Another way to look at it is to see that, every point has been brought down 1 unit!

I think you'll find a useful answer here: http://socratic.org/trigonometry/graphingtrigonometricfunctions/translatingsineandcosinefunctions
Vertical translation
Graphing
#y=sinx+k# Which is the same as#y=k+sinx# :In this case we start with a number (or angle)
#x# . We find the sine of#x# , which will be a number between#1# and#1# . The after that, we get#y# by adding#k# . (Remember that#k# could be negative.)This gives us a final
#y# value betwee#1+k# and#1+k# .This will translate the graph up if
#k# is positive (#k>0# )
or down if#k# is negative (#k<0# )Examples:
#y=sinx#
graph{y=sinx [5.578, 5.52, 1.46, 4.09]}#y=sinx+2 = 2+sinx#
graph{y=sinx+2 [5.578, 5.52, 1.46, 4.09]}#y=sinx4=4+sinx#
graph{y=sinx4 [5.58, 5.52, 5.17, 0.38]}The reasoning is the same for
#y=cosx+k=k+cosx# , but the starting graph looks different, so the final graph is also different:#y=cosx#
graph{y=cosx [5.578, 5.52, 1.46, 4.09]}#y=cosx+2 = 2+cosx#
graph{y=cosx+2 [5.578, 5.52, 1.46, 4.09]}