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.

Algebra ->  Test -> 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.      Log On


   

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) About Me  (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.
~~~~~~~~~~~~~~~~~~~~~ 

3%2Atan%5E2%28theta%29+%2B1 = 4%2Atan%28theta%29  --->

3%2Atan%5E2%28theta%29+-+4%2Atan%28theta%29+%2B+1 = 0  ---->  (factor the left side)  --->

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


This equation deploys in two independent equations:


1)  -3tan%28theta%29%2B1 = 0  --->  3tan%28theta%29 = 1  --->  tan%28theta%29 = 1%2F3  --->  

     Two solutions of this equation are  

         a)  theta = acrtan%281%2F3%29 = 0.32175 radians = 18.444 degrees,  and

         b) theta = acrtan%281%2F3%29+%2B+pi = 180 degs + 18.444 degs = 198.444 degs


2)  -tan%28theta%29%2B1 = 0  --->  tan%28theta%29 = 1    

     Two solutions of this equation are  

         a)  theta = 45 degrees,  and

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


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