Solving Inverse Function: sec(2x+180)=2, 0<x<360

[Link]

I can only find two answers for this equation, whereas the books says it should be four. Can someone enlighten me? Showing the procedure would help:P

(degrees)
sec(2x+180) = 2 0<x<360

 

[Galileo]

First write it as cos(2x+180)=1/2.

Then get rid of the 180 (the 180 causes a shift in the graph of cos(2x)).

 

[OlderDan]

First write it as cos(2x+180)=1/2.

Then get rid of the 180 (the 180 causes a shift in the graph of cos(2x)).

Changing to cosine is a good idea, but you can't get rid of 180 and get the right answers for x. You could change the cosine to -cos(2x) = 1/2, or set the argument of the cosine as it stands to the values that have cosine = 1/2, then solve for x, keeping only the solutions in the specified interval.

 

[Galileo]

You could change the cosine to -cos(2x) = 1/2

That's what I meant by 'getting rid of the 180'.

 

[whkoh]

Check the range of x:
0 < x < 360
180 < 2x + 180 < 900