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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
3+sec%5E2%28x%29-3+=+0+
3%28sec%5E2%28x%29-1%29=0
Dividing by 3 to get an equivalent equation we get
sec%5E2%28x%29-1=0
Factoring we get
%28sec%28x%29%2B1%29%28sec%28x%29-1%29=0--->system%28sec%28x%29=-1%2C%22or%22%2Csec%28x%29=1%29
sec%28x%29=1%2Fcos%28x%29=-1<--->cos%28x%29=-1 corresponds to highlight%28x=pi%29%29%29%29%0D%0A%7B%7B%7Bsec%28x%29=1%2Fcos%28x%29=1<--->cos%28x%29=1 corresponds to highlight%28x=0%29 .
The graphs of red%28cos%28x%29%29 and green%28sec%28x%29%29 look like this

x=2pi is also a solution, but is not within the interval %22%5B+0+%2C%222pi%22%29%22 , because the%22%29%22 next to 2pi means x%3Cpi .
highlight%28x=0%29 and highlight%28x=pi%29 are the only two solutions with 0%3C=x%3Cpi .
The smaller solution is highlight%28x=0%29 and the larger one is highlight%28x=pi%29 .

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.