SOLUTION: 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.

Question 1068189: 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.
Answer by ikleyn(52805) (Show Source): You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~~~~~~

 =   --->

 = 0  ---->  (factor the left side)  --->

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


This equation deploys in two independent equations:


1)   = 0  --->   = 1  --->   =   --->  

     Two solutions of this equation are  

         a)   =  = 0.32175 radians = 18.444 degrees,  and

         b)  =  = 180 degs + 18.444 degs = 198.444 degs


2)   = 0  --->   = 1    

     Two solutions of this equation are  

         a)   = 45 degrees,  and

         b)  = 180 degs + 45 degs = 225 degs.


Answer.  18.444 degs, 45 degs, 198.44 degs nd 225 degs.

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SOLUTION: Solve 3tan^2&#952; + 1 = 4tan&#952; for all positive angles less than 360�. Give answers in increasing order. All values should be in degrees. Round to the nearest degree.

SOLUTION: 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.