Question

Pre-cal 12 Question!


0≤θ<2π This is the limit!

Can this affect the angles of general solution?

Answer 1

This is one of the angles.

\[\theta 1= \frac{ \pi }{2 }\]

Answer 2

Second angle:

\[\theta 2= \frac{ 3\pi }{2 }\]

Answer 3

The General solution is :

\[\theta 1 + 2\pi(n) , n \in I\]

\[\theta 2 + 2\pi(n) , n \in I\]

Answer 4

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.

Answer 5

wow those r a lot

Answer 6

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.

Answer 7

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.

Answer 8

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. :)