Question 1068189
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Solve 3tan^2θ + 1 = 4tanθ for all positive angles less than 360°.

Give answers in increasing order. All values should be in degrees. Round to the nearest degree.
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<pre>
{{{3*tan^2(theta) +1}}} = {{{4*tan(theta)}}}  --->

{{{3*tan^2(theta) - 4*tan(theta) + 1}}} = 0  ---->  (factor the left side)  --->

(-3tan(theta)+1)*(-tan(theta)+1) = 0.


This equation deploys in two independent equations:


1)  {{{-3tan(theta)+1}}} = 0  --->  {{{3tan(theta)}}} = 1  --->  {{{tan(theta)}}} = {{{1/3}}}  --->  

     Two solutions of this equation are  

         a)  {{{theta}}} = {{{acrtan(1/3)}}} = 0.32175 radians = 18.444 degrees,  and

         b) {{{theta}}} = {{{acrtan(1/3) + pi}}} = 180 degs + 18.444 degs = 198.444 degs


2)  {{{-tan(theta)+1}}} = 0  --->  {{{tan(theta)}}} = 1    

     Two solutions of this equation are  

         a)  {{{theta}}} = 45 degrees,  and

         b) {{{theta}}} = 180 degs + 45 degs = 225 degs.


<U>Answer</U>.  18.444 degs, 45 degs, 198.44 degs nd 225 degs.
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