Sir,
For the following question: y=cos' pi/2x ....... I read this as y= cos ((pi/2)x)
You read this correctly. pi / 2 x means pi / 2 * x; according to the order of operations you divide pi by 2 then multiply the result by x.
which means that the omega is pi/2 where upon the period of the cycle is T=(2pi/(pi/2)), therefore T=4..
This is correct. When you go through a complete cycle of the cosine function your values go from 1 to 0 to -1 then back to 0 and finally return to the original 1. These values should occur between x = 0 and x = 4, with the cycle repeated between x = 4 and x = 8, between x = 8 and x = 12, etc..
Cycles will also occur between x = -4 and x = 0, between x = -8 and x = -4, etc..
You can relate this to the q_a_ strategy of asst 2. If you make a table of cos(theta) vs. theta you will get the usual y values. If you then solve pi / 2 * x = theta for x you get x = 2 / pi * theta.
When I graph this, it looks very queer..I'm not sure as to how to interpret the period T=4 since, till this point we have been dealing with (Pi radians)...
Also for the question y=Cos x +1, I read this as y=cos(x)+1; meaning this function has a vertical shift of one..
This is correct. In the order of operations a function like sin, cos, log, etc. has the same status as a multiplication: it applies to what follows it, and it precedes addition.