Trig identities

[pinklemonade]

Hey guys, I have a pretty simple question but it's confusing me a lot right now as I cant find the answer

It says:
Solve the following equations over the interval . Give your answers correct to 2 decimal places

a. sec(x)=-4

I've already solved for x and got 1.32 radians, however when it comes to getting the answer I dont understand why the it is not
and

Instead the answer is x=1.82 and x=-1.82

Bit confusing to explain, but can someone help please !

Thank you

[nerdgasm]

Hmm, I think I can see what has happened here. Your method, while perhaps somewhat inelegant, might actually work out (though I would recommend the simpler, solving for sec(x) = -4 method).

Would I be right in saying that what you have done, is this?

You have solved for (essentially solving for ). You then noted that in general, . Therefore, since when   , you reasoned that when , , thus solving the original equation,

This method is not incorrect in and of itself. In fact, you managed to obtain one correct solution!

Notice that your solution of IS actually (approximately) equal to . So that solution is fine. For your second solution, notice that you have gone outside the domain mentioned by the question. You would want , which does indeed give you .