# *HELP*Investigate Values of m in lR where cosx=mx has 2 Solutions

1. Jan 15, 2009

### AnnaSuxCalc

1. The problem statement, all variables and given/known data

(a)Carefully draw graphs of y=cosx, y=x, y=(1/5)x
(b) From the graphs, determine how many solutions the equation cosx=mx has for m=1 and m=1/5
(c) Add a sketch of y=mx onto your picture, where m is chosen so that cosx=mx has exactly two solutions. (without computing the value of m)
(d) Use your sketch to estimate the correct value of m
(e) why is it true that the value of -m will also give exactly two solutions to cosx=mx?
(f)Is it possible to find a value of m such that cosx=mx has exactly three solutions? four? n?
Explain by sketching y=cosx and y=mx for relevant values of m

3. The attempt at a solution
A hint was given to us by the prof:
"you should draw all your graphs on just one diagram like: (the attachment)"

Okay, so I don't have a problem drawing the graphs,but for part (b) and rest
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

• ###### Picture 1.png
File size:
7.3 KB
Views:
108
2. Jan 15, 2009

### HallsofIvy

If you are able to do a, why does your 'attempt at a solution' not show that at least?
If you can in fact draw the graph in (a) all you have to do to answer (b) is look at that graph and count the number of times one graph crosses the other.