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Science Forum Index » Optics Forum » please tell me!!
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| H-U Chou |
 Posted: Sun Nov 02, 2003 10:12 pm |
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Hi
I have a question about approximation.
In what condition, we can let "tan(theta)=theat"
please give me an order number in angle
Or tell me how to evaluate?
thanks!! |
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| Phil Hobbs |
| Posted: Sun Nov 02, 2003 10:12 pm |
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H-U Chou wrote:
Quote: I have a question about approximation.
In what condition, we can let "tan(theta)=theat"
please give me an order number in angle
It's considered bad manners to ask people to do your homework for you.
It also won't do you any good.
Look up the Maclaurin series for tangent, and your question will answer
itself.
Cheers,
Phil Hobbs |
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| Repeating Decimal |
| Posted: Sun Nov 02, 2003 11:31 pm |
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in article bo4gjk$2bc3$1@news.ncu.edu.tw, H-U Chou at s1226036@cc.ncu.edu.tw
wrote on 11/2/03 7:12 PM:
Quote: Hi
I have a question about approximation.
In what condition, we can let "tan(theta)=theat"
please give me an order number in angle
Or tell me how to evaluate?
thanks!!
Look on a slide rule. Compare the S, T, and ST scales. That would be a good
graphical indication.
Bill |
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| West Coast Engineering |
| Posted: Mon Nov 03, 2003 9:39 am |
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"H-U Chou" <s1226036@cc.ncu.edu.tw> wrote:
Quote: Hi
I have a question about approximation.
In what condition, we can let "tan(theta)=theat"
please give me an order number in angle
Or tell me how to evaluate?
thanks!!
Let's say you are doing all your calculations to 10 significant
figures. Then I would say that:
tan(theta)-theta(in radians) should be kept less than 1.0D-15 to avoid
excessive round off problems.
Slide rule? Gees, you're as old as I am. |
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| West Coast Engineering |
| Posted: Mon Nov 03, 2003 9:40 am |
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Repeating Decimal <salmonfry@sbcglobal.net> wrote:
Quote: in article bo4gjk$2bc3$1@news.ncu.edu.tw, H-U Chou at s1226036@cc.ncu.edu.tw
wrote on 11/2/03 7:12 PM:
Hi
I have a question about approximation.
In what condition, we can let "tan(theta)=theat"
please give me an order number in angle
Or tell me how to evaluate?
thanks!!
Look on a slide rule. Compare the S, T, and ST scales. That would be a good
graphical indication.
Bill
Slide Rule? Oh, a posting from an old F@^ like me.  |
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| West Coast Engineering |
| Posted: Mon Nov 03, 2003 9:41 am |
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"H-U Chou" <s1226036@cc.ncu.edu.tw> wrote:
Quote: Hi
I have a question about approximation.
In what condition, we can let "tan(theta)=theat"
please give me an order number in angle
Or tell me how to evaluate?
thanks!!
When I was a your optical designer, we didn't even have slide rules,
we had to count on our fingers, and we LIKED IT THAT WAY. |
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| Richard F.L.R. Snashall |
| Posted: Mon Nov 03, 2003 9:59 am |
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West Coast Engineering wrote:
Quote: "H-U Chou" <s1226036@cc.ncu.edu.tw> wrote:
Hi
I have a question about approximation.
In what condition, we can let "tan(theta)=theat"
please give me an order number in angle
Or tell me how to evaluate?
thanks!!
When I was a your optical designer, we didn't even have slide rules,
we had to count on our fingers, and we LIKED IT THAT WAY.
But you weren't s'posed to wear'm clean off! |
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| Harvey |
| Posted: Mon Nov 03, 2003 11:33 am |
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Guest
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The series for Sin(x) & Cos(x) are extremely well known, one can use
tan=sin/cos & the binomial theorem to derive the first terms in a series for
Tan(x) in a few seconds.
You then compare the value of the first term (which is 'x' of course) to the
value of the second to derive the accuracy of the approximation.
It takes a matter of seconds to do it, so I'll leave you to work out the
power of x & its coefficient in the second term yourself!
Its interesting however that the sin & cos series are commonplace, but the
tan series rarely quoted.
Harvey
"West Coast Engineering" <westcoastengineering@westcoastengineering.com>
wrote in message news:nvpcqv8e085ekp057cgtn8tgkirr8e03or@4ax.com...
Quote: "H-U Chou" <s1226036@cc.ncu.edu.tw> wrote:
Hi
I have a question about approximation.
In what condition, we can let "tan(theta)=theat"
please give me an order number in angle
Or tell me how to evaluate?
thanks!!
Let's say you are doing all your calculations to 10 significant
figures. Then I would say that:
tan(theta)-theta(in radians) should be kept less than 1.0D-15 to avoid
excessive round off problems.
Slide rule? Gees, you're as old as I am.
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| Phil Hobbs |
| Posted: Mon Nov 03, 2003 6:06 pm |
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Bob May wrote:
Quote: Half a degree is good enough for a level of accuracy. Don't let the
poopooers get you down.
Wow, 9 followups to a very simple homework question! Are we bored, or what?
Back on your heads.
Cheers,
Phil Hobbs |
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| Bob May |
| Posted: Mon Nov 03, 2003 8:02 pm |
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Guest
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Half a degree is good enough for a level of accuracy. Don't let the
poopooers get you down.
--
Bob May
Losing weight is easy! If you ever want to lose weight, eat and drink less.
Works evevery time it is tried! |
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| Bob May |
| Posted: Tue Nov 04, 2003 4:53 pm |
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7 followups mentioning that it is homework, two giving different answers in
different ways.
Since the guy is probably gone now, I'll note that my answer is wrong.
Doing homework by internet deserves wrong answers.
--
Bob May
Losing weight is easy! If you ever want to lose weight, eat and drink less.
Works evevery time it is tried! |
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