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Think about the polar co-ordinate notation \((r, \theta)\), where r stands for the radius, or distance from the origin to the point, and \(\theta\) stands for the angle from the \(x\)-axis.
Look at the drawing. Can the the radius change, and still be at the same point?
Can the angle change and still be at the same point at the end?
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Answer the questions separately. Think about the radius one first, and tell me your answer.
well I feel like in order for it get back to its place it would have to be ((2pi+1)pi)
Remember, \(2\pi\) always gets you back to where you began. In fact, any even multiple of \(pi\) will do that. So, as long as the radius is 4, if you watnt to get back, what should the multiples of \(\pi \) be?
oh so it just needs to be 2npi because it just needs twice to get back? @jlvm
Yes. That's one of the two options.
When \(r\) is positive, in this case \(r=4\) that is the case. Now, what about when \(r=-4\)?
that's when it's going to have to switch to 2n+1)pi right?