SOLUTION: I have no idea how to start this problem. Ca you please help. Use a graphing utility to approximate the solutions of the equation in the interval [0, 2π). If possible, find th

Algebra ->  Trigonometry-basics -> SOLUTION: I have no idea how to start this problem. Ca you please help. Use a graphing utility to approximate the solutions of the equation in the interval [0, 2π). If possible, find th      Log On


   

Question 770001: I have no idea how to start this problem. Ca you please help. Use a graphing utility to approximate the solutions of the equation in the interval [0, 2π). If possible, find the exact solutions algebraically. (Enter your answers as a comma-separated list.)
9 tan 2x − 18 cos x = 0
x =
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
               9tan(2x) − 18cos(x) = 0

Divide through by 9

                 tan(2x) − 2cos(x) = 0

                    sin%282x%29%2Fcos%282x%29 - 2cos(x) = 0

                %282sin%28x%29cos%28x%29%29%2F%281-2sin%5E2%28x%29%29 - 2cos(x) = 0

Divide through by 2

                 %28sin%28x%29cos%28x%29%29%2F%281-2sin%5E2%28x%29%29 - cos(x) = 0

Multiply through by LCD of 1 - 2sinē(x)

sin(x)cos(x) - cos(x)(1 - 2sinē(x)) = 0

Factor out cos(x)

     cos(x)[sin(x) - (1 - 2sinē(x)] = 0

      cos(x)[sin(x) - 1 + 2sinē(x)} = 0

Use the zero-factor property:

cos(x) = 0;            sin(x) - 1 + 2sinē(x) = 0

x = pi%2F2, 3pi%2F2;            2sinē(x) + sin(x) - 1 = 0     

                   [2sin(x) - 1][sin(x) + 1] = 0

               2sin(x) - 1 = 0            sin(x) + 1 = 0       
                   2sin(x) = 1                sin(x) = -1 
                    sin(x) = 1%2F2                     x = 3pi%2F2
                         x = pi%2F6, 5pi%2F6  

There are 4 solutions in  [0, 2π).

               pi%2F6, pi%2F2, 5pi%2F6, and 3pi%2F2                             

Edwin