(2tan^2(x))-(2tan(x))=3

Question

find, to the nearest degree, all positive values of X less than 360. thank you for the help.

Answer 1

2tan²(x) - 2tan(x) = 3

 

 

Subtract 3 on both sides of equation.

 

2tan²(x) - 2tan(x) - 3 = 0

 

 

Use the quadratic formula to solve for tan(x).

 

tan(x) = (2 ± √(4 - 4(-6))) / 4

tan(x) = (2 ± √(28)) / 4

tan(x) = (2 ± 5.29) / 4

 

tan(x) =  (2 + 5.29) / 4                 and               tan(x) = (2 - 5.29) / 4

 

tan(x) = 1.83                               and                tan(x) = -0.83

 

x = 61                                        and                     x = -40

 

 

Tangent is only positive in the 1st and 3rd quadrant.  In the other quadrants, tangent is negative.

 

x = 180 + 61                                                       x = 180 - 40

   = 241                                                                 = 140

                  

                                                                              x = 360 - 40

                                                                                 = 320

 

We have 4 solutions.

 

x = 61

x = 140

x = 241

x = 320