SOLUTION: Find the amplitude, period, and phase shift and sketch the graph. y = {{{1/2}}}sin(x + <font face = "symbol">p</font>)

Rule:

For either y = A*sin(Bx+C) or y = A*cos(Bx+C)

Amplitude = |A|
Period = 2p/B
Phase shift = C/B and if that is positive the phase 
shift is left and if negative the phase shift is right.

y = sin(x + p)

A = , B = 1, C = p.  that is positive,
so the shift will be left.

Amplitude = |A| =  = 
Period = 2p/B = 2p/1 = 2p = 4p
Phase shift = C/B =  = p.

But first we will draw the graph unshifted which is the graph of
y = sin(x)

without the +p term.



The above is the graph of one period of y = sin(x) between
the two green bars. Notice that this basic period starts at 0 and 
ends to 2p.
Notice that the x-intercepts are at 0, p,
and 2p 

The curve rises to
 and drops to  which is because its amplitude is .

Now since the equation is y = sin(x + p)
and not y = sin(x), we shift it to the left by p units.  The x-intercept at 0 
moved left to -p
and the x-intercept at p moved to 0 and the x-intercept at 2p
moved p units left to p. 

    

Edwin