suppose i have a function sin(sin x)

sin x will give values [-1,1] ...

so now, should i take these values in degree or radian to find sin(sin x) ?

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- Mar 4th 2011, 03:10 AMcupidDegree or Radian?
suppose i have a function sin(sin x)

sin x will give values [-1,1] ...

so now, should i take these values in degree or radian to find sin(sin x) ? - Mar 4th 2011, 03:41 AMFernandoRevilla
The standard "geometric" definition for:

$\displaystyle \sin:\mathbb{R}\to [-1,1],\quad x\to \sin x$

$\displaystyle \cos: \mathbb{R}\to [-1,1],\quad x\to \cos x$

is when $\displaystyle x$ is "measured" in radians. So we have good properties, for example:

**(i)**$\displaystyle (\sin)'=\cos$

**(ii)**$\displaystyle \sin x=x-x^3/3!+x^5/5!-\ldots\quad (\forall x\in \mathbb{R}) $

etc. - Mar 4th 2011, 11:14 AMPerfessor
I believe you want radians.

- Mar 5th 2011, 01:19 AMHallsofIvy
The

**only**time you should use degrees is when the problem specifically gives angles in degrees. For problems in which sine (or cosine) is used just as a**function**always use radians.

(There are a number of ways to define sine and cosine that do not involve**angles**at all. So strictly speaking the argument is not in "radians" or "degrees". However, to be able to identify those functions with the sine and cosine functions we learned in trigonometry, we use radians.) - Mar 6th 2011, 04:12 AMcupid
- Mar 6th 2011, 04:29 AMPlato
- Mar 6th 2011, 07:56 AMcupid
- Mar 6th 2011, 08:02 AMPlato
- Mar 6th 2011, 08:10 AMcupid
but my question is that ... for example i have a question ... sin (sin x)

i need to calculate the value of this function at $\displaystyle x = \frac{\pi}{2}$

as $\displaystyle sin\frac{\pi}{2} = 1$

now i need to calculate sin(1)

so should i find value of sin(1 radian) or sin(1 degree) ??? - Mar 6th 2011, 08:19 AMPlato
- Mar 6th 2011, 11:29 AMcupid
- Mar 6th 2011, 11:48 AMTheEmptySet
The point that I think you are missing is that Radians are a pure number! They are defined as the arc length of a circle divided by the radius of the same circle so strictly speaking the "units" (length) reduce out leaving a Real number.

Radian - Wikipedia, the free encyclopedia - Mar 6th 2011, 12:14 PMHallsofIvy
Yes, that was what I was trying to say to begin with!

"Strictly speaking the argument is not in "radians" or "degrees". However, to be able to identify those functions with the sine and cosine functions we learned in trigonometry, we use radians."