Question 1209153
<pre>
Ikleyn took the denominator as

(sin(b)×(x-π)),  as it was typed.  

However, I purposely changed it to 

(sin(b(x-π)).

She tried to solve this problem using f(x) as it was written:

{{{f(x)}}}{{{""=""}}}{{{(k+x^3sec^""(x))/(sin^""(b)*(x-pi) ) )}}}

and found that it was unsolvable for b by ordinary mathematical means.

However, I assumed the student had mistyped, and that f(x) should have been
this instead: 

{{{f(x)}}}{{{""=""}}}{{{(k+x^3sec^""(x))/(sin^""( b*(x-pi) ) )}}}

By making this change, I was able to solve for b using the quadratic formula.

Why did I assume that the student has mistyped?

I reasoned that no professional math problem-creator would have included 
only one sine function of a constant, in this case, sin(b).  If a professional
problem-creator included a sine function, they certainly would have used a sine
function of a VARIABLE, not the sine of a CONSTANT, which would be a constant
itself!  So I changed the denominator so that the sine function would be of a
variable, not of a constant.

Also, no professional math problem-creator would create a problem that would
not be solvable by ordinary means taught in normal calculus courses.

So I changed the denominator (sin(b)×(x-π)) to (sin(b(x-π)) and was able to
solve for b using the quadratic formula.

It made more sense to me that a typo had been made, rather than an incompetent
math-problem-creator -- especially since there was a typo of a missing right
parenthesis in this: 

4(π^(5/ 2    

which Ikleyn mentioned.

Also, when a problem contains k, this letter is nearly always taken as an
arbitrary constant, but Ikleyn found k not to be arbitrary at all.  

I think my interpretation was the intended problem.  Maybe Ikleyn will agree
with me on that.  

Edwin</pre>