Question 1078936
Definitions:

y = A cos(Bx + C) + D
----------------------
amplitude = A
period = 2π/B
phase shift = −C/B
vertical shift = D
----------------------
{{{ y = -cos( x/4 - pi/2 ) }}}
--------------------------
{{{ D = 0 }}}
so, the vertical shift is {{{ 0 }}}
---------------------------
{{{ A = -1 }}}
so, the amplitude is {{{ -1 }}}
( same as the regular amplitude, except inverted )
---------------------------
{{{ -C/B = (-(-pi/2))/(1/4) }}}
{{{ -C/B = 4*(pi/2) }}}
{{{ -C/B = 2*pi }}}
So, the phase shift is {{{ 2*pi }}}, which is 360 degrees,
which means there is no phase shift at all.
---------------------------
{{{ (2*pi)/B = (2*pi)/(1/4) }}}
{{{ (2*pi)/B = 8*pi }}}
so, the period is {{{ 8*pi }}} 
-------------------------
The range is from {{{ -1 }}} to {{{ +1 }}} which is {{{ 2 }}}
-------------------------
Here is the plot over 2 periods, or {{{ 16*pi }}}
{{{ graph( 400, 400, -30, 30, -2, 2, -cos( x/4 - pi/2 ) ) }}}
( note that a period of {{{ 8*pi = 25.13 }}}
which is about what I see on the plot )