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Inverse Trig Functions

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Mon May 30, 2011 7:21 pm
Ranger Hawk says...



So I'm trying to work on these inverse trig problems, and the range/domain of the graphs is giving me a lot of trouble. For example, one of my problems is this:

4 cos^2*x - 1 = 0

and I've gotten it to

x = cos^(-1)(1/2)

and I've even graphed it on the unit circle and found that, based on the fact that cosine's range is from zero to pi, the two solutions should be: 1. 2pi/3 + n*pi, where n is an integer, and 2. pi/3 -- but here's my problem. The answer in the back of the book says it should simply be added to n*pi, but wouldn't it be 2n*pi? Because if you take a pi rotation on the unit circle from pi/3, it brings you to the cosine value of negative 1/2, and I'm looking for the positive values.

I really hope this all makes sense; let me know if you need more clarification. Thanks in advance for any help!

Edit: Never mind. Went to the tutor center and got the answer (for those of you who are wondering, I forgot to put the positive/negative 1/2, so I needed to find both instances of that).
Last edited by Ranger Hawk on Tue May 31, 2011 10:27 pm, edited 1 time in total.
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