Question 448478
Find the amplitude, period, and phase shift.

y = 10*cos(½x)

<pre><font face = "consolas" color = "indigo" size = 4><b>
Rule:

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

Amplitude = |A|
Period = 2<font face = "symbol">p</font>/B
Phase shift = C/B and if that is positive the phase 
shift is left and if negative the phase shift is right.

y = 10*cos(½x)

y = 10*cos(½x+0)

A = 10, B = ½, C = 0.

Amplitude = |A| = |10| = 10
Period = 2<font face = "symbol">p</font>/B = 2<font face = "symbol">p</font>/½ = 2<font face = "symbol">p</font>*2 = 4<font face = "symbol">p</font>
Phase shift = C/B = 0/½ = 0 (No phase shift).

{{{drawing(400,400,-.9,4pi+.5,-11,11,
graph(400,400,-.9,4pi+.5,-11,11, 10cos(x/2)), green(line(0,0,0,10),line(2pi,0,2pi,-10),line(4pi,0,4pi,10)),
locate(pi,1,pi),locate(2pi-.4,1,2pi),locate(3pi-.7,1,3pi),
locate(4pi-.7,1,4pi),



circle(pi,0,.1), circle(2pi,0,.1), 
circle(3pi,0,.1), 
circle(4pi,0,.1) 


)}}}

This is the graph of one period of y = 10*cos(½x).
Notice that it goes from 0 to 4<font face = "symbol">p</font>.
Notice that the x-intercepts are at 0, <font face = "symbol">p</font>,
2<font face = "symbol">p</font>, 3<font face = "symbol">p</font>, and 4<font face = "symbol">p</font> 

Notice that the three green lines are 10 units each,
which is the amplitude.

Edwin</pre>