Question 971803
.
For the equation
cos(5 x) = −1
find the smallest solution, the largest solution and the number of solutions for x in the interval 0 ≤ x ≤ 2π.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~



        Regarding this problem, I'd like to make two comments.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;First, &nbsp;in &nbsp;Math text, a professional Math writer would never write for such problem &nbsp;&nbsp;0 <= x <= 2π.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A professional writer will write &nbsp;&nbsp;0 <= x < 2π.  &nbsp;Find the difference.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Second, the solution and the answer in the post by @lwsshak3 are incorrect.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For correct solution, &nbsp;see my post below.



<pre>
cos(5x) = -1

5x = π, 3π, 5π, 7π, 9π, . . . 

x = {{{pi/5}}}, {{{3pi/5}}},  {{{5pi/5}}} = π,   {{{7pi/5}}},  {{{9pi/5}}}, . . . 


For greater or smaller values of 5x,  values of x will be out of the given interval.


So, there are 5 solutions to the given equation in interval 0 <= x < 2π.


The smallest is  {{{pi/5}}}.  The greatest is  {{{9pi/5}}}.  The number of solutions is 5.    <U>ANSWER</U>
</pre>

Solved correctly.


I am surprising to see so elementary error in the post by @lwsshak3.