# Solve f(x)=sin(x/2)

matt grime
Homework Helper
Please don't take this the wrong way, but why don't you know the properties of sin (and cos etc) when you're expected to work out all these things. I don't see how you've got to be in a situation like this where you need to ask what the derivative of x/2 is.

This isn't me saying 'gosh, how can someone not know *that*' but asking 'how can someone who doesn't know that be in a class that asks them to find the points of inflexion of sin(x/2)'?

I have this sketch pad program and it does it automatically, but i'm not sure how. first derivative is instead of the /4 it is /2

Tom Mattson
Staff Emeritus
Gold Member
Why are you using a program? This is easy to do without one.

Here are two hints:

If $u$ is a differentiable function of $x$ then we have:

$$\frac{d}{dx}\sin(u)=\cos(u)u'$$
$$\frac{d}{dx}\cos(u)=-\sin(u)u'$$

As for the derivative of $\frac{x}{2}$ simply recall that $\frac{x}{2}=\frac{1}{2}x$ and use the appropriate differentiation rule.

matt grime
Homework Helper
you're using a computer program for this??? cough, splutter, ahem, various 'what's the world coming too' noises. This question is the equivalent of asking what 2+2 is, really, which is why I would really like to understand the set of circumstances that has led you to need to answer this question and not understand how to differentiate x/2

I don't know why there is a 2 and a 4 at the end and a -1 in front...i know that sinx=cosx and that cosx=-sinx..?

frenkie said:
I don't know why there is a 2 and a 4 at the end and a -1 in front...i know that sinx=cosx and that cosx=-sinx..?

NO!!!

It is absolutely not true that

sin(x) = cos(x) for all x.

or

cos(x) = -sin(x) for all x.

Do you understand what the problem is with what you wrote.

However it is true that teh first derivative of sin(x) is equal to cos(x) and that the first derivative of cos(x) is equal to -sin(x).

Tom Mattson
Staff Emeritus
Gold Member
frenkie said:
I don't know why there is a 2 and a 4 at the end and a -1 in front...

I gave you the differentiation rules. Have you tried to use them? If so then present your work and we'll show you what's wrong with it.

i know that sinx=cosx and that cosx=-sinx..?

No. Put a derivative operator in front of the left side of each of those equations, and then they will become true.

how do you find end behavior of the function sin(x/2)

frenkie said:
how do you find end behavior of the function sin(x/2)

What do you know about the function y = sin(x)?

Surely the behavior of y = sin(x/2) should be similar..

end behavior is a straight line going to negative and positive infinity?

frenkie said:
end behavior is a straight line going to negative and positive infinity?

What are you talking about? What does the graph of the function y = sin(x) look like?

its an even graph going up to 1 and down to -1...

HallsofIvy
Homework Helper
No, it's not. Since your idea of solving math problems appears to be punching calculator keys, more or less at random, how about graphing sin(x) on a calculator and looking at it?

arildno
Homework Helper
Gold Member
Dearly Missed
As a follow-up to Halls' suggestion, let Xmin=-20, Xmax=20, Ymin=-1, Ymax=1 (on the Window menu).

What does the graph tell you?

it tells you that the roots of sin(x/2) are at -2Pi, o and 2Pi? this is HARD!

frenkie said:
it tells you that the roots of sin(x/2) are at -2Pi, o and 2Pi? this is HARD!

Yes... But there are a lot more zeros than that... What do you know about the sine function?

well its an even function...limits at negative and positive infinity...root at zero? what do u mean when u say there are alot more zeros?

frenkie said:
well its an even function...limits at negative and positive infinity...root at zero? what do u mean when u say there are alot more zeros?

How can you be asking these questions when you are supposed to be finding the extrema of this function? Surely you must be in a calculus class, and in my experience most calculus classes require some prerequisite knowledge of trigonometry and trigonometric functions. You do realize that the sine funtion is a trigonometric fundtion right?

Next, What does it mean mathematically for a function to be even? Because f(x) = sin(x) is absolutely not an even function.

If a function is even it satisfies the following equlity.
f(x) = f(-x)
graphically this means that the function is symmetric about the y axis.

I have no clue what you mean by "limits at positive and negative infinity" because you give no context for them in the post I have quoted.

And when I say there are a lot more than three zeros, I specifically mean that there are an infinite number of zeros for the function y = sin(x/2) just as there are of the function y = sin(x). If you do not know this you are in no position to be speaking of the limits as x goes to positive or negative infinity, or finding the local extrema of this function. I suggest that you do a bit of research on the sine function before you make any more attempts at this problem.

can u tell me what is greater then 2Pi on a unit circle? please. thats what i need to know.

frenkie said:
can u tell me what is greater then 2Pi on a unit circle? please. thats what i need to know.

what is greater then 2Pi on a unit circle? it has nothing to do with this problem, i just need to know.

what is greater then 2Pi on a unit circle? it has nothing to do with this problem i just need to know.

frenkie said:
what is greater then 2Pi on a unit circle? it has nothing to do with this problem, i just need to know.

It would really help if you would give some context as to what you are talking about, however I would suppose that 3pi, 4pi, 5pi, 1729pi etc.. would all be greater that 2pi...

HallsofIvy