Radian measure- Small angle approximations
I might just be being silly here.
In this example where I have drawn the arrow. If I’m not mistaken, when you take the 4 out of the bracket it would mean that it would be come 4^-1(1-x²/4)?? Were as the textbook as stated over 2?
I have tried to find some questions in the textbook to verify but I haven’t found any.
In this example where I have drawn the arrow. If I’m not mistaken, when you take the 4 out of the bracket it would mean that it would be come 4^-1(1-x²/4)?? Were as the textbook as stated over 2?
I have tried to find some questions in the textbook to verify but I haven’t found any.
(edited 1 year ago)
Yes youre correct. They may have meant (theta/2)^2 (it isnt written like that, but being generous) but not checked as it doesnt affect the answer.
tbh, on line 2, Id have divided top and bottom by 2 to give 1-... on the denom which is what you want. They multiply by 2 then divide by 4. Seems error prone.
tbh, on line 2, Id have divided top and bottom by 2 to give 1-... on the denom which is what you want. They multiply by 2 then divide by 4. Seems error prone.
(edited 1 year ago)
Original post by mqb2766
Yes youre correct. They may have meant (theta/2)^2 (it isnt written like that, but being generous) but not checked as it doesnt affect the answer.
tbh, on line 2, Id have divided top and bottom by 2 to give 1-... on the denom which is what you want. They multiply by 2 then divide by 4. Seems error prone.
tbh, on line 2, Id have divided top and bottom by 2 to give 1-... on the denom which is what you want. They multiply by 2 then divide by 4. Seems error prone.
Thank you for confirming my argument. This book honestly has a lot of errors and for a Cambridge edition( if any relation to the school) , is appalling.
It makes you question yourself a lot of the time, especially if you’re not 100% confident in your own abilities.
Edit:
Doesn’t affect the outcome as we’re ignoring theta² and above, however, if we were included then the the second expansion would have been incorrect.
(edited 1 year ago)
Original post by mqb2766
Yes youre correct. They may have meant (theta/2)^2 (it isnt written like that, but being generous) but not checked as it doesnt affect the answer.
tbh, on line 2, Id have divided top and bottom by 2 to give 1-... on the denom which is what you want. They multiply by 2 then divide by 4. Seems error prone.
tbh, on line 2, Id have divided top and bottom by 2 to give 1-... on the denom which is what you want. They multiply by 2 then divide by 4. Seems error prone.
Wouldn’t this approach be a lot simpler.
Original post by mqb2766
Yes, its even simpler if you don't multiply top and bottom by 2 in the first place, and just divide them by 2.
Lol. The example doesn’t really teach anything useful to be fair.
Original post by KingRich
Lol. The example doesn’t really teach anything useful to be fair.
A good example of dumb algebra, where you do algebra without thinking why/if it will help. And it would be easy to see that a series expansion of the denominator would be 2 + O(theta^2), so its not even worth thinking about it as youre multiplying by theta and hence neglecting it. So 4theta/2.
(edited 1 year ago)
Original post by mqb2766
A good example of dumb algebra, where you do algebra without thinking why/if it will help. And it would be easy to see that a series expansion of the denominator would be 2 + O(theta^2), so its not even worth thinking about it as youre multiplying by theta and hence neglecting it. So 4theta/2.
Lol. I agree. I have done this in the past as I have been learning as you’ve probably noticed over the time of helping me. As I am growing though, I have started thinking logically and looking for the quickest route.
Not always confident in some of my answers but that’s the benefit of this website
always someone to assist in your thinkingQuick Reply
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