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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: pinklemonade on February 19, 2015, 10:19:35 pm

Title: Trig identities
Post by: pinklemonade on February 19, 2015, 10:19:35 pm: 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 $[-\pi ,\pi ]$ . 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
$x=\pi-1.32$ and $x=\pi+1.32$

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

Bit confusing to explain, but can someone help please !

Thank you
Title: Re: Trig identities
Post by: nerdgasm on February 19, 2015, 11:06:16 pm: 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 $sec(x) = 4$ (essentially solving for $cos(x) = \frac{1}{4}$ ). You then noted that in general, $cos(x) = -cos(x+ \pi)$ . Therefore, since when $cos(x) = \frac{1}{4},$ $x = \pm 1.32$ , you reasoned that when $x = \pm 1.32 +\pi$ , $cos(x) = \frac{-1}{4}$ , thus solving the original equation, $sec(x) = -4.$

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

Notice that your solution of $x = \pi - 1.32$ IS actually (approximately) equal to $1.82$ . So that solution is fine. For your second solution, notice that you have gone outside the domain mentioned by the question. You would want $1.32 - \pi$ , which does indeed give you $-1.82$ .