korosh23
  • korosh23
Pre-cal 12 Question! 0≤θ<2π This is the limit! Can this affect the angles of general solution?
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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korosh23
  • korosh23
This is one of the angles. \[\theta 1= \frac{ \pi }{2 }\]
korosh23
  • korosh23
Second angle: \[\theta 2= \frac{ 3\pi }{2 }\]
korosh23
  • korosh23
The General solution is : \[\theta 1 + 2\pi(n) , n \in I\] \[\theta 2 + 2\pi(n) , n \in I\]

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korosh23
  • korosh23
My question is, any value of n cannot be placed since we have a limit of 0≤θ<2π. only +1 can be replaced by n. Am I right? Please explain.
anonymous
  • anonymous
wow those r a lot
zepdrix
  • zepdrix
All values of n form a "general solution" when no restriction is placed on theta. Since we have a restriction placed on our angle, \(\large\rm 0\le\theta<2\pi\), then only specific values of n will satisfy the solution set. Namely, n=0 gives us our only two solutions.
zepdrix
  • zepdrix
I'm not sure what you meant by `only +1 can be replaced by n.` if you meant only 1 can be replaced by n, it looks like that doesn't work out. \[\large\rm \frac{\pi}{2}+2\pi (1)>2\pi\] only 0 can be replaced by n.
korosh23
  • korosh23
Yes, I understand it now. The general solution can be affected by the limit. You are right, only 0 can be replaced by n in this situation. Thank you for checking my work. :)

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