QUESTION on trig graphs (1 Viewer)

[GirlGoneMad]

Ok, I am unsure what they actually want here:

what features can be determined about the sine graph from the graph of it's derivative (cosine graph) and the graph of it's second derivative

do they mean its period and amplitude are the same, or that it has shifted or that its turning points are zero and points at zero are turning points

do they want me to talk about how the derivative of sinx is cosx and the second derivative of sinx is -sinx?

 

[kpq_sniper017]

Originally posted by GirlGoneMad
Ok, I am unsure what they actually want here:

what features can be determined about the sine graph from the graph of it's derivative (cosine graph) and the graph of it's second derivative

do they mean its period and amplitude are the same, or that it has shifted or that its turning points are zero and points at zero are turning points

do they want me to talk about how the derivative of sinx is cosx and the second derivative of sinx is -sinx?

well, u can tell from the graph of its derivative that it will periodic. when the derivative is 0, then the original curve will have a local max or a local min.....etc.

 

[GirlGoneMad]

so I should write about that then...stupid maths...you never know exactly what they want you to discuss so on most of my assessments I write too much...

 

[kpq_sniper017]

Originally posted by GirlGoneMad
so I should write about that then...stupid maths...you never know exactly what they want you to discuss so on most of my assessments I write too much...

i can't be exactly sure that that is what the question is asking, but its only my own interpretation.
is it an isolated question, or is part of a whole question? coz that might give u more of an idea of what they're asking.

 

[:: ck ::]

Originally posted by GirlGoneMad
Ok, I am unsure what they actually want here:

what features can be determined about the sine graph from the graph of it's derivative (cosine graph) and the graph of it's second derivative

do they mean its period and amplitude are the same, or that it has shifted or that its turning points are zero and points at zero are turning points

do they want me to talk about how the derivative of sinx is cosx and the second derivative of sinx is -sinx?

Take y=sinx
for the graph of it's derivative, the graph becomes
y' = cosx
which you can prolli ramble on about how it is the same graph of y=sinx, however shifted left by pi/2 units.. or more accurately through the identity :
cosx = sin(pi/2-x) ... = sin[-(x-pi/2)] = -sin(x-pi/2)]

it is the graph of y=sinx ... shifted to the right pi/2 units... then reflected in the x axis

then for second derivative, y'' = -sinx

u can say it is the same graph as y=sin x reflected about the x axis

the period and amplitude is not changed when taking both the first and second derivatives of y=sinx ...

 

[Seraph]

oo well now that this is up i may as well ask this

Okay withotu any differentation or anything

how do id raw y = cos(x + pi/4)

i know Period = 1 and amplitude = 2pi right??

But with the pi/4 what does that mean?

 

[kpq_sniper017]

Originally posted by Seraph
oo well now that this is up i may as well ask this

Okay withotu any differentation or anything

how do id raw y = cos(x + pi/4)

i know Period = 1 and amplitude = 2pi right??

But with the pi/4 what does that mean?

that means that the graph is translated pi/4 to the left
+ = translated left
- = translated right

 

[kpq_sniper017]

btw.
when u draw it, shift the axis and not the graph....generally makes things easier.

 

[CM_Tutor]

Originally posted by Seraph
how do id raw y = cos(x + pi/4)

i know Period = 1 and amplitude = 2pi right??

Actually, the period is 2π and amplitude is 1

 

[Eagles]

Originally posted by GirlGoneMad
what features can be determined about the sine graph from the graph of it's derivative (cosine graph) and the graph of it's second derivative

huh?
like all derivatives (and calculas).. isn't it just:

f (x) tell the position
f ' (x) tell the gradient(velocity)
f " (x) tell the points of inflexion(acceleration)

of the original graph???

 

[:: ck ::]

yes but with trig graphs u can talk about something special...

... possibly something to do with SHM and the relationship between displacement and acceleration ?

/shrug