3U Maths Question Thread

[jamonwindeyer]

I'm inputting 2000^2 x (tan(13)^2 - tan(15)^2)   Is this correct?

Ahh, not quite:



The fraction behaves a little differently than what you've assumed, try doing the values of cot in the denominator separately, and THEN putting them into the fraction!

You can't just flip the fraction as a whole, you have to flip the two individually and stick them on the denominator in this case

[kevin217]

Ahh, not quite:



The fraction behaves a little differently than what you've assumed, try doing the values of cot in the denominator separately, and THEN putting them into the fraction!

You can't just flip the fraction as a whole, you have to flip the two individually and stick them on the denominator in this case

Ok yeah now I got it, thanks.

[imtrying]

Could someone explain the working for this question? I've indicated where I'm getting lost...I think maybe I'm  lacking an understanding of factorials or something? Because I'm just not seeing how those last couple of lines of working work:/

[jakesilove]

Could someone explain the working for this question? I've indicated where I'm getting lost...I think maybe I'm  lacking an understanding of factorials or something? Because I'm just not seeing how those last couple of lines of working work:/

Hey! Jamon actually JUST showed the simplification of that line, in a slightly different form. Check it out here! You can factorise it a little to get it into the 1-(etc) form that is in the answers you've provided. Once you get it into the required simplified form, it becomes fairly clear that this equals the RHS. Does that make sense? Happy to expand on my answer if you need it!

[imtrying]

Hey! Jamon actually JUST showed the simplification of that line, in a slightly different form. Check it out here! You can factorise it a little to get it into the 1-(etc) form that is in the answers you've provided. Once you get it into the required simplified form, it becomes fairly clear that this equals the RHS. Does that make sense? Happy to expand on my answer if you need it!

I've had a look at that other post, I see that I need to get a common denominator, in this case (k+2)!but just don't understand how to change 1/(k+1)! to make that common denominator? 

[jakesilove]

I've had a look at that other post, I see that I need to get a common denominator, in this case (k+2)!but just don't understand how to change 1/(k+1)! to make that common denominator?

Ah fair enough! We multiply the top and the bottom by (k+2). So,

[Cindy2k16]

I've had a look at that other post, I see that I need to get a common denominator, in this case (k+2)!but just don't understand how to change 1/(k+1)! to make that common denominator?

Does this help?

[jakesilove]

Does this help?

Beautiful! That's exactly right, thanks Cindy!

[imtrying]

Ah fair enough! We multiply the top and the bottom by (k+2). So,

Does this help?

Thank you that helped so much!

[Blissfulmelodii]

Just a quick question. I'm really struggling with sketching inverse functions. Just wondering what the steps are to sketch them and if there are things that we should remember.
Also how do you find the domain and range for an inverse function when there is a coefficient in front of the x for example sin(2x) or sin(x/2)??
Thanks in advance

[znaser]

Substitute in the values of the turning points:




The point of interest is that top one; we will only have two zeroes if THAT function value falls below or on the x axis. Otherwise, it turns back around to soon and we are stuck with a single zero, as required. Therefore, we need:



That was actually a little trickier than it appeared on first glance does it make sense why I've done what I've done?

Yep i get it  Thanks!

[kevin217]

Just a quick question. I'm really struggling with sketching inverse functions. Just wondering what the steps are to sketch them and if there are things that we should remember.
Also how do you find the domain and range for an inverse function when there is a coefficient in front of the x for example sin(2x) or sin(x/2)??
Thanks in advance

For Domain: sin^-12x                               sin^-1(x/2)
                 −1 ≤ 2x ≤1                             −1 ≤ x∕2 ≤1
                 −½ ≤ x ≤ ½                             −2 ≤ x ≤ 2
In terms of range, it would still be the same as sin^-1x.

[Rikahs]

Btw a trick to find the range is to sub in those extreme points of the domain e.g. 1/2 and -1/2 into the inverse equation and they will give you the two end points for the range

[jamonwindeyer]

Just a quick question. I'm really struggling with sketching inverse functions. Just wondering what the steps are to sketch them and if there are things that we should remember.
Also how do you find the domain and range for an inverse function when there is a coefficient in front of the x for example sin(2x) or sin(x/2)??
Thanks in advance

Hey Bliss! So sketching an inverse is really a turnaround question; because the first thing we should always do is just draw the regular function first (even if its in our heads or on a scribble). Then, we just reflect it about the line \(y=x\) as we'd expect. Note also that your domain and range should swap places!! So if the range of your original function is \(y>0\), then the domain of your inverse will be \(x>0\). As a final tip, remember that your function and its inverse should only ever intersect on the line y=x. If they cross elsewhere, you've missed something.

Never try and sketch a function without its inverse; it's just too tricky, unless it is something you recognise. For example, you might be able to sketch the inverse of an exponential straight away, because it will be a logarithm

Inverse trig functions are tougher, but it's not terrible. Remember what the basic shapes are (inverse sine, inverse cos, and inverse tangent), and then adjust your typical parameters just like Kevin showed you above. You know typically that what's inside an inverse sine function can range from -1 to 1; that sets up those inequalities

Practice makes perfect with these; the more you do the easier it gets!

PS - Great work above Kevin and Rikahs

[anotherworld2b]

Can i please get help with these two questions please? I am not sure how projectile works