Need help solving the following equations on the interval (0,2pi)?

Question

I'm having a lot of trouble trying to solve the equations algebraically on the interval (0,2pi). Any help is greatly appreciated!

 

1) tanx= 0

 

2) 4sin^2x-1=0

Answer 1

Question 1

 

tan(x) = 0

 

We can rewrite this in terms of sine and cosine.

 

(sin(x)) / (cos(x)) = 0

 

We set sin(x) = 0

 

  x = 0

 

 

Question 2

 

4sin²x - 1 = 0

 

We factor this using the FOIL method.

 

(2sin(x) + 1)(2sin(x) - 1) = 0

 

We set   2sin(x) + 1 = 0         and         2sin(x) - 1 = 0

 

             2sin(x) = -1                and         2sin(x) = 1

 

             sin(x) = -1/2               and         sin(x) = 1/2

                  x = -π/6                 and               x = π/6

 

The only value of x that is in the interval (0, 2π)  is x = π/6.

 

We accept x = π/6.