find the limit

bgbgbgbg · Hodge Conjecture Offline Joined: 17 Sep 2009 Posts: 97

find the limit:
lim (sinx)/x as x goes to 0 if x in degrees

**Posted:** Tue Oct 27, 2009 8:52 pm

tobeno_1

**Posted:** Tue Oct 27, 2009 8:59 pm

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bgbgbgbg · Hodge Conjecture Offline Joined: 17 Sep 2009 Posts: 97

notice that x in degrees not in radian

**Posted:** Tue Oct 27, 2009 9:16 pm

evoluciona · New Member Offline Joined: 27 Oct 2009 Posts: 10

**Posted:** Tue Oct 27, 2009 9:22 pm

phymax

it doesnt even count much in hyperreals.

**Posted:** Fri Oct 30, 2009 7:04 am

mavropnevma

$\lim_{x \to 0} \frac {\sin x} {x} = 1$ . It does not matter the unit of measure for $x$ , be it radians, degrees (or maybe $\textrm{Fahrenheit}^{\circ}$ Smile

).

**Posted:** Fri Oct 30, 2009 11:30 pm

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shyong

it would makes sense if you could tell what is the meaning of a real number divided by a degree ?

**Posted:** Sat Oct 31, 2009 12:08 am

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jmerry

Given the level of understanding this question was asked at, the last few posts really don't fit.

There is a perfectly sensible $\sin$ function defined on angles, which can be measured in degrees. Before calculus, degrees are as good as any angle measurement system, and cive us nice numbers for nice angles.
So, now we want to develop the calculus of trigonometric functions. The first crucial limit that comes up is this one: what is $\lim_{x\to 0}\frac{\sin x}{x}$ . Since we don't know any better, that angle is marked in degrees for now. What is the value of this limit? Some ugly number; if we look closer, it turns out to be $\frac{\pi}{180}$ .
We don't like that, so we invent an entirely new angle measurement, called the radian. Scaling the angle measurement changes the limit, and for the radian's arclength scaling it turns out to be $1$ .
That is the point of radians. From there on, we never use degrees in a calculus setting again.

**Posted:** Sat Oct 31, 2009 12:35 am