find the -intercepts of the trigonometric equation plz help !!!!!!!!!!

Question

Find the -intercepts of the  trigonometric equation : .

Answer 1

The equation is .

To find the x - intercept then y = 0.

Let , the function has a period of , first find all solutions in the interval .

The function is negative in second and third quadrant; and the function is positive in first and fourth quadrant.

So the solutions are ; and substitute in .

Answer 2

To check for extraneous solutions, the solutions, are substitute in .

                                               (Substitute )

                                                     (Solution does not check)

                                         (Substitute )

                                                      (Solution checks)

                                         (Substitute )

                                                  (Solution does not check)

                                         (Substitute )

                                                 (Solution checks)

In four possible solutions are extraneous.

So, in the interval , the only two solutions are .

Finally, add multiples of to each of these solutions to get the general form

where n is integer.

   (Substitute )

                        (Divide each side by )

The solutions are .