<PRE><B>Question 786565</B>
tan x + &amp;#8730;3= 0 &amp;#8594; tan x =&amp;#8722;&amp;#8730;3

 The term tan x is now isolated in the equation. Find a particular solution on the interval (0, &amp;#960;).
x =2&amp;#960;/3 , 0 &lt; x &lt; &amp;#960; 

On (-Infiniti, infiniti ), there are an infinite number of solutions. Write the general form of the solution. Your answer should be exact. (Use n as an integer constant. Enter your response in radians.) 
 x=???????????
&lt;pre&gt;
Since tangent has period &lt;font face=&quot;symbol&quot;&gt;p&lt;/font&gt;, we can add any 
positive, negative, or zero multiple of &lt;font face=&quot;symbol&quot;&gt;p&lt;/font&gt; to 2&lt;font face=&quot;symbol&quot;&gt;p&lt;/font&gt;/3.

Answer = 2&lt;font face=&quot;symbol&quot;&gt;p&lt;/font&gt;/3 + n&lt;font face=&quot;symbol&quot;&gt;p&lt;/font&gt;.

You could get an LCD of 3, and then factor out &lt;font face=&quot;symbol&quot;&gt;p&lt;/font&gt; on top and get {{{(2+3n)pi/3}}}, but that is not necessary.

Edwin&lt;/pre&gt;

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