# Thread: I don't get how to do this >_<

1. ## I don't get how to do this >_<

Another question about differentiating a trigonometric function except I was away when they taught how to do it and I really am very bad at it.

a) Find the equation of the tangent to the curve y = sinx at the origin

I know this should be pretty straight foward but as I said I'm really bad at this kind of stuff.

b) Using a graph or otherwise, state the number of solutions to the equation sinx = x

c) Let m be a positive number. For what set of values does the equation sinx = mx have exactly 3 solutions satisfying
-π ≤ x ≤ π
[I'm not sure if this is only my computer but those signs there on the last line should be pi's because on my computer some weird symbol is coming up]

2. Hello
Originally Posted by sweetG
Another question about differentiating a trigonometric function except I was away when they taught how to do it and I really am very bad at it.

a) Find the equation of the tangent to the curve y = sinx at the origin

I know this should be pretty straight foward but as I said I'm really bad at this kind of stuff.
The equation of the tangent to the curve of a function $\displaystyle f$ at a point $\displaystyle a$ is $\displaystyle y=f(a)+(x-a)f'(a)$. In your case, $\displaystyle a=0$ (origin) and $\displaystyle f(x)=\sin x$ hence the equation of the tangent you're looking for is $\displaystyle y=\sin 0+(x-0)\sin '(0)=\ldots$

b) Using a graph or otherwise, state the number of solutions to the equation sinx = x
Using a graph is a good idea. The solutions of $\displaystyle \sin x =x$ are the intersection points of the curves of the two functions $\displaystyle x\mapsto x$ and $\displaystyle x\mapsto \sin x$. How many such point(s) can you find ?

[I'm not sure if this is only my computer but those signs there on the last line should be pi's because on my computer some weird symbol is coming up]
I see the symbol $\displaystyle \pi$.

3. Hi,

given function is y=sinx

diff with respect to x
dy/dx=cosx
dy/dx at (0,0) = cos0=0

now, we have to find the equation of the tangent formula is (y-y1)=dy/dx(x-x1)
since x1=0 and y1=0
plug all the values in the above formula

y-0=0(x-0)

---Rk

4. Thanks I got the first bit but I'm still very confused about the two last bits (b) and (c). Does anyone know how to do them ?
By the way 'm' is tangent.

5. Originally Posted by sweetG
Thanks I got the first bit but I'm still very confused about the two last bits (b) and (c). Does anyone know how to do them ?
Why are you confused about the second question ? Did you sketch the graph of the two functions ?

6. Am I supposed to sketch y = sinx and y = x ? Because if so then wouldn't they intersect at many points ?! =S I'm so confused

7. Sorry guys I made a mistake for part (b), it hits x = 0, x = π and x = - π, right ?

Hmm not sure what to do for part (c) though.

8. Originally Posted by sweetG
Am I supposed to sketch y = sinx and y = x ? Because if so then wouldn't they intersect at many points ?! =S I'm so confused
No, there is only one intersection point.

Originally Posted by sweetG
Sorry guys I made a mistake for part (b), it hits x = 0, x = π and x = - π, right ?
No. $\displaystyle \sin \pi =0\neq \pi$. Again, did you sketch the graph of the two functions ? If you did, why did you find the solutions $\displaystyle x=\pm\pi$ ? (there is no intersection point for $\displaystyle x=\pi$ )

Hmm not sure what to do for part (c) though.
Originally Posted by sweetG
c) Let m be a positive number. For what set of values does the equation sinx = mx have exactly 3 solutions satisfying [/B] -π ≤ x ≤ π
I suggest you sketch the graphs of $\displaystyle x\mapsto \sin x$ and of $\displaystyle x\mapsto mx$ for several values of $\displaystyle m$. (say $\displaystyle m=4,\,m=2,\,m=1,\,m=1/2,\,m=1/4,\,m=1/10\ldots$) Using this you should be able to find for which values of $\displaystyle m$ the equation $\displaystyle \sin x=mx$ has exactly three solutions in $\displaystyle [-\pi:\pi]$. (the answer is an interval, for $\displaystyle m$ sufficiently small, $\displaystyle \sin x=mx$ has always three solutions in $\displaystyle [-\pi,\pi]$)