Arccos(16x)=arcsec(x) solve for x?

Question

I just don't have any idea how to go about this

Answer 1

The domain of the Arccosine is the range of cosine = [-1,1].

 

So, for Arccos(16x), -1≤16x≤1.  Therefore, -1/16≤x≤1/16.

 

The domain of the Arcsecant is the range of the secant =

   [1,∞)∪(-∞,-1]

 

So, for Arcsecx, x ≥ 1 or x ≤ -1. 

  

Thus, the equation Arccos(16x) = Arcsecx has NO SOLUTION.  

 

 

Answer 2

arccos is the same as 1/cos.  arcsec is the same as 1/sec, which is then cos.
 
1 / cos(16x) = cos(x)
 
 
Multiply both sides of the equation by cos(16x).
 
1 = cos(x)cos(16x)
 
 
We know that cos(0) is 1.  So cos(0)cos(0) is 1.  The value of x that will make this true is
 
x = 360n

 

where n is all integers.