Question 803454
<pre>
cos(4x)=0

The angles with cosine 0 are all the odd multiples of {{{pi/2}}}

4x = {{{(2n+1)pi/2}}}

 x = {{{(2n+1)pi/2}}}÷4
 x = {{{(2n+1)pi/2}}}{{{""*""}}}{{{1/4}}}
 x = {{{(2n+1)pi/8}}} 

 {{{pi<=(2n+1)pi/8<=2pi}}}

Divide all three sides by <font face="symbol">p</font>

 {{{1<=(2n+1)/8<=2}}}

Multiply all three sides by 8 to clear of fractions:

 {{{8<=2n+1<=16}}}

Subtract 1 from all three sides

 {{{7<=2n<=15}}}

Divide all three sides by 2

 {{{3.5<=n<=7.5}}}

Since n is an integer
 
  {{{4<=n<=7}}}, 

  n &#8712; {4,5,6,7}

Answers:  x = {{{(2(4)+1)pi/8}}} = {{{(8+1)pi/8}}} = {{{9pi/8}}} 
          x = {{{(2(5)+1)pi/8}}} = {{{(10+1)pi/8}}} = {{{11pi/8}}} 
          x = {{{(2(6)+1)pi/8}}} = {{{(12+1)pi/8}}} = {{{13pi/8}}} 
          x = {{{(2(7)+1)pi/8}}} = {{{(14+1)pi/8}}} = {{{15pi/8}}} 

Edwin</pre>