solutions for cos (1 Viewer)

[blackbunny]

Show that the transcendental equation cos(x) = x has a solution for 0 <= x <=pi/2

can i just graph it, caz from the graph u can see the answer right away

 

[shafqat]

i guess so if the question doesnt exclude it
i cant think of any 3u techniques to solve it
anyway i think the intermediate value thm is assumed in this course

 

[blackbunny]

the only thing i can think of is graph it.

 

[nit]

Yep, I think the best way is to use the intermediate value theorem, which is the same thing as graphing it, so either a table of values or a rough sketch should suffice.

Edit: Newton's method may be of some use in locating the zero as well.

Shafqat: we get around to proving it at uni this year.

 

[Will Hunting]

Is the question followed up by something like this:

... Hence, graph cos(x) = x, showing all necessary features

If so, you'll probably need to use another method.

 

[Slidey]

f(x)=cosx-x

f(x) is continuous
f(0) = 1 > 0
f(pi/2) = -pi/2 < 0

Since f(x) is continuous, and changes sign on the [0,pi/2], a root exists on this interval.

 

[blackbunny]

y in the world do i have to find the root. all i have to do is to show if f(x) has solutions 0<x<pi