Hi, I'm new here. I'm a homeschooled senior in my last leg of pre-graduation math stress. Stupidly, I decided to take a pre-calculus class, and found out exactly how far it is beyond my scope of learning capability the hard way.
Anyway, I need help!
Solve exactly. 4sin^2x -3=0, 0 greater than or equal to x, x less than 2pi.
Sorry for not using the proper signs, I'm not sure where to find them on the keyboard. By "pi", I mean Pi. Not just two random variables strung together.
And please, don't think I haven't done any work on this problem--I've spent the last two days trying to find a page in my textbook that will shed light upon the matter, to no avail. None of the examples quite match the construction of this problem, and after flying through a myriad different starting points, all of which became tangled, I'm still just as lost as if I'd never started. It's the only reason I'm not showing any work. :P
First, solve forSolve exactly: .
We have: .
Take square roots: .
At this point, we are expected to be familiar with some special angles.
. . We should know the trig values for 30°, 60°, and 45°.
And we recognize that: .
From there, we know that: .
Wow. I just had that "OOOOOH" feeling you get when something suddenly clicks.
Thank you both tremendously! Soroban, I totally forgot about radians (which explains why the answer in the book was so weird!) and Dan, that's an excellent way to think of it. So much simpler.
All right... I need some help again, regarding the same subject.
The problem looks like this:
It says to "Solve exactly without the use of a calculator".
What I don't understand, or have forgotten through lack of use, is how you solve a sin or cosine without the use of a calculator? Is this another problem concerning radian measure?
Would it be possible for someone to solve a similar problem to this one, so I can see from the example how it's to be done?