SOLUTION: Hello! I need help solving this: Find all solutions of the equation in the interval [0, 2π). 3 sec^2 x − 3 = 0 What is the smaller and what is the larger val

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Question 978429: Hello!
I need help solving this:
Find all solutions of the equation in the interval
[0, 2π).
3 sec^2 x − 3 = 0
What is the smaller and what is the larger value?
Found 2 solutions by htmentor, KMST:
Answer by htmentor(1343)   (Show Source): You can put this solution on YOUR website!
3 sec^2 x − 3 = 0 -> 3(sec^2 x - 1) = 0 -> sec^2 x - 1 = 0 -> 1/cos^2 x - 1 = 0
Multiply through by cos^2 x:
1 - cos^2 x = 0
sin^2 x = 0
sin x = 0
The solutions are x=0, x=π on the interval [0, 2π)
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!


Dividing by 3 to get an equivalent equation we get

Factoring we get
--->
<---> corresponds to <---> corresponds to .
The graphs of and look like this

is also a solution, but is not within the interval , because the next to means .
and are the only two solutions with .
The smaller solution is and the larger one is .

NOTE:
I got a thank you message from you for my answer to a different question.
In that thank you, you were asking
"So I have the samller value 0 and what is the larger one?"
I am guessing that thank you was for htmentor's answer of this question.
I had not answered this question before I got your thank you.
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