[MOVED] solve tan(x) + sec(x) = sqrt[3] on [0, 2pi]

[ladyfire]

Hey. I have about 20 problems each like the other. If you could show me how to do one, then I could probably figure the others out. Thanks!

Solve the following equation in the interval [0, 2pi]:

. . .tan(x) + sec(x) = sqrt[3]

I don't really know what it's asking me to do. I remember doing stuff like this in Trig, but that was a long time ago.
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Edited by stapel -- Reason for edit: categorization, spelling

 

[skeeter]

Re: Derivatives

delete bogus solution ... my apologies.

 

[stapel]

I have about 20 problems each like the other. If you could show me how to do one, then I could probably figure the others out.

If you have twenty trig equations to solve and have no idea how to start any of them, then you may need more review (re-teaching) than we can provide within this context. Thanks!

tan(x) + sec(x) = sqrt[3]

I don't really know what it's asking me to do.

The question is asking you to find the values of "x" that make the equation true, similar to every other sort of "solve the equation" exercise you've done. The only difference is that you're working with trig functions, instead of quadratics or whatever.

There are probably many ways to approach this, but I'd probably start with changing everything to sines and cosines. Then square both sides. You should be able then to apply an identity and a difference-of-squares factoring to get:


. . . . .[1 + sin(x)] / [1 - sin(x)] = 3

Cross-multiply, simplify, and solve.

Eliz.