Question 882509
<pre>
y = a·sin[b(x+c)] + d  or y = a·cos[b(x+c)] + d   

amplitude = |a|
period = {{{2pi/b|||
phase shift = |c| right if c negative, left if c positive
vertical shift = |d| up if d positive, down if d negative

{{{matrix
(1,3,
y,""="",expr(1/2)cos(5pi*x-3))}}}

Factor out {{{5pi}}}

{{{matrix
(1,3,
y,""="",expr(1/2)cos((5pi)(x-3/(5pi))))}}}

compare to

y = a·cos[b(x+c)] + d  

{{{matrix(1,4,    a=1/2, b=5pi, c=3/5pi, d=0 )}}}

amplitude = |a| = {{{abs(1/2)||| = {{{1/2}}}
period = {{{2pi/b}}} = {{{(2pi)/(5pi)=2/5}}}
phase shift = |c| = {{{abs(-3/(5pi))}}} right since negative
vertical shift = |d| = 0 so no vertical shift

Edwin</pre>