Intermediated Value Problem, Stumped!

[Guest RyanL]

As a question last class our prof threw this one to us;

 

Use the intermediated value theorem to show that there is some angle theta radians btw 0 and pi that sintheta=theta + 1

 

After looking at this however either I'm missing something really basic or this problem isn't right. No angle theta would fufill that equation because sin can only be 1, so theta would have to equal 0, and sin(0) isn't 1. Is there something I'm missing or did the prof mess up?

[Dave]

I think you may be looking at it the wrong way

 

Look at that equation for a minute. We can't use the IVT on an equation, so you need to define a function f(t) = sin(t) - t -1, and then because we're looking between 0 and pi, have f : [0,pi] -> R.

 

f(0) = -1 and f(pi) = pi - 1. Moreover, f(pi) > f(0). So you should be able to apply the IVT from here.

[bloodhound]

but , sinx = x + 1 doesnt have a positive real solution. that is obvious from drawing the two graphs.

[Dave]

There is that.

 

I swear I'm getting worse and worse at maths