Mathematics Question Thread

[gilliesb18]

Can someone help me understand the Hyperbola? How to sketch it and how to work out the domain and range?? I'm confused!! Thanks...

[1937jk]

okay so i'm doing something very wrong here, I keep getting zero and can't figure out why,
Find the area bounded by the curve y = cos2x, the x axis and the lines x = 0 and x = pi 

[RuiAce]

Can someone help me understand the Hyperbola? How to sketch it and how to work out the domain and range?? I'm confused!! Thanks...

Please provide an example.

(Alternatively there was an example done a few days ago but that may require going back a few pages, so you may provide your own example)

okay so i'm doing something very wrong here, I keep getting zero and can't figure out why,
Find the area bounded by the curve y = cos2x, the x axis and the lines x = 0 and x = pi 

[RuiAce]

Hi! Could i get help with this question. Not sure whether me or my peer is right :/

[michaelalt]

Hi can someone else help with q.3?

[jamonwindeyer]

Hi can someone else help with q.3?

Sure! So we first differentiate using the normal rule for tan:



Now we want to find the gradient at \(x=\frac{\pi}{9}\), we get that by substituting into our derivative:



Now we find the y-coordinate of our point by substitution into the original function - It ends up being \(y=\sqrt{3}\). So we put all that into the point gradient formula:



And that should be the answer! Does that make sense?

[1937jk]

[/quote]

ohhh Thank you so much!!!!

[RuiAce]

I need some help with this question.
It says to find the volume of the solid around the y-axis.
The answer I got was 64pi/15, but the textbook answer was 16pi/15.
I double checked my working out and can't find any errors.

In the future please post your working so we can look for any potential errors.

[asd987]

Hi, can i get some help with ii)

[jamonwindeyer]

Hi, can i get some help with ii)

Hey! So all you are doing here is finding when \(v=0\), using the expression from (i)!



Notice that I've taken only the smallest positive answer to the trig equation, because want the first time it has come to rest. Does this make sense?

[asd987]

so this is supposed to be the answer
I don't understand how -1/2 becomes 7pi/12 when you move sin on the other side?

[RuiAce]

so this is supposed to be the answer
I don't understand how -1/2 becomes 7pi/12 when you move sin on the other side?

[jamonwindeyer]

so this is supposed to be the answer
I don't understand how -1/2 becomes 7pi/12 when you move sin on the other side?

so this is supposed to be the answer
I don't understand how -1/2 becomes 7pi/12 when you move sin on the other side?

Oh yep that's totally the answer, I made an error above (I'll go back and fix it up). So we are here:



What we do then is think, okay, what must \(2t\) be to give a result of \(\frac{-1}{2}\). We turn to angles of any magnitude, all stations to central. We know that sine is negative in the third and fourth quadrants (we only care about the third). We also know that \(\sin{\frac{\pi}{6}}=\frac{1}{2}\). Put that together:



This is something you first did with degrees in Year 11

[katnisschung]

quickest way to sketch superimposition of 2 graphs??
(e.g. cos2x + sin2x) i just do a table of values and put it into my calculator (i don't show working)
cos otherwise the table would be like 3 rows
thanks

also if a hsc q asks u to sketch a graph what details MUST u show (e.g. x-intercepts for trig?)

[jamonwindeyer]

quickest way to sketch superimposition of 2 graphs??
(e.g. cos2x + sin2x) i just do a table of values and put it into my calculator (i don't show working)
cos otherwise the table would be like 3 rows
thanks

Hey! Fastest way to sketch a superposition is to do a quick sketch of the two graphs in light pencil, then draw the superposition of the two in a darker pen (possibly erasing the other curves too) - For the example you provided for example, those are two curves that are fairly easy to sketch - It is faster to just quickly bump those out and then add them up visually rather than muck around with your calculator, at least in my opinion

also if a hsc q asks u to sketch a graph what details MUST u show (e.g. x-intercepts for trig?)

You should always show whatever details they ask for (at minimum), and besides that, whatever is necessary such that it is clear what graph you are sketching. For example, if asked to sketch a parabola, just the y-intercept isn't enough. You'd want either a turning point/vertex, or roots. You should also take into account the ease with which the points are found - For example, when sketching a cubic, you usually won't need to find x-intercepts unless they are made obvious to you, because finding roots of cubics is quite tedious for the most part