Question 388645
Need your help please! 
In the interval 0° ≤ θ ≤ 360°, how many values of θ satisfy the equation 
{{{Tan^2theta-3Tan(theta) + 2 = 0}}} 
a)1 
b)2
c)3
d)4
<pre>
{{{Tan^2theta-3Tan(theta) + 2}}}{{{""=""}}}{{{0}}}

Factor the left side:

{{{(Tan(theta)- 2)(Tan(theta)-1)}}}{{{""=""}}}{{{0}}}

Use the zero-factor principle:

{{{Tan(theta)-2}}}{{{""=""}}}{{{0}}}
{{{Tan(theta)}}}{{{""=""}}}{{{2}}}

Since the tangent is positive in the first and third quadrants,
there are two angles between 0° and 360° that have 2 as their 
tangent.  These are 63.43° and 243.43° approximately

Continuing with the zero-factor principle:

{{{Tan(theta)-1}}}{{{""=""}}}{{{0}}}
{{{Tan(theta)}}}{{{""=""}}}{{{1}}}
 
Again, since the tangent is positive in the first and third quadrants,
there are two angles between 0° and 360° that have 1 as their 
tangent.  These are 45° and 225° exactly.

So the answer is d)4

Edwin</pre>