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Edexcel Core 3 - 21st June 2016 AM

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Original post by 1 8 13 20 42
I haven't made a proper go at it (should be revising not going back to try tricky a level stuff lol) but on playing around with stuff I find it depends on the values of theta which seems to not be what was intended..

Spoiler



I am pretty sure this can be done completely through identities. My LaTeX isn't working on TSR so:

Spoiler

(edited 7 years ago)
Original post by Euclidean
Find real values of λ and μ such that:



If anyone has a go, please spoiler solutions :smile:


I know this isn't that good a solution, but could you substitute some values (θ\theta = 0, π2\frac\pi2) and get some simulatenous equations which you can use to work out λ\lambda and μ\mu. Another solution I tried didn't seem to work when I substituted values for theta back in.
Original post by Craig1998
I know this isn't that good a solution, but could you substitute some values (θ\theta = 0, π2\frac\pi2) and get some simulatenous equations which you can use to work out λ\lambda and μ\mu. Another solution I tried didn't seem to work when I substituted values for theta back in.


I am not sure, my proposed solution seems incredibly flawed at the moment so I'm not sure whether my question actually has any real solutions...

Here's what I thought initially:


Original post by Euclidean
I am pretty sure this can be done completely through identities. My LaTeX isn't working on TSR so:

Spoiler

Original post by Euclidean
I am pretty sure this can be done completely through identities. My LaTeX isn't working on TSR so:

Spoiler



What I did led to I think sole potential solutions

Spoiler

Original post by Euclidean
I am not sure, my proposed solution seems incredibly flawed at the moment so I'm not sure whether my question actually has any real solutions...

Here's what I thought initially:


Incidentally this is very reminiscent of a problem I had in my analysis paper yesterday which involved as a sub-part showing that there is only one root of cosx = sinx in [0,pi/2]

Note yet another edit

Spoiler

(edited 7 years ago)
Guys anyone know if this question is even in our syllabus lol C3 Solomon paper K, question 4b.
Original post by 1 8 13 20 42
What I did led to I think sole potential solutions

Spoiler



This is true, I hadn't considered that sin(2x)=/=-1 etc. Although, where I initially modified the problem from (M4 paper) the angle theta is acute.


Original post by 1 8 13 20 42
Incidentally this is very reminiscent of a problem I had in my analysis paper yesterday which involved as a sub-part showing that there is only one root of cosx = sinx in [0,pi/2]

Note yet another edit

Spoiler



It's quite interesting that mu and lambda are now functions of theta rather than constants, that also completely skipped my mind.
Original post by Euclidean
This is true, I hadn't considered that sin(2x)=/=-1 etc. Although, where I initially modified the problem from (M4 paper) the angle theta is acute.




It's quite interesting that mu and lambda are now functions of theta rather than constants, that also completely skipped my mind.


Fair enough, although it seems to avoid any kind of case analysis 2theta ought to be acute. Yeah, it's an interesting symptom of periodic behaviour/the relationship between sin and cos.
Original post by mathsmann
Guys anyone know if this question is even in our syllabus lol C3 Solomon paper K, question 4b.


Not sure, but I think the solution for this is quite easy anyway (plus I love proof).

Spoiler

Original post by Craig1998
Not sure, but I think the solution for this is quite easy anyway (plus I love proof).

Spoiler



i see thanks a lot
when sin(theta) =-1/2 , can anyone tell me what the theta values will be because the theta values im getting are wrong apparently :s-smilie:
Original post by mathsmann
when sin(theta) =-1/2 , can anyone tell me what the theta values will be because the theta values im getting are wrong apparently :s-smilie:


Should get 210 and 330 as the first 2 values on the positive x side.
Original post by particlestudent
Should get 210 and 330 as the first 2 values on the positive x side.


Oops i meant cos(x +45)=-0.75, I wrote the wrong question lol , what values would u get if you were given that and the range was from -pi to +pi
Original post by Lilly1234567890
Can someone explain to me what this question means..

Given that the equation f(x) = k where k is a constant, has exactly two roots.
state the range of possible values of k.

What does that mean?


1465663927667.jpg
f(x) = k
So f(x) - k = 0
K transforms f(x) by shifting it down by k units. We need to find the value of k which will mean f(x) will intersect with the x axis in two places. In the graph I've attached, if k is 1, the graph will have one root, meaning that as long as k > 1, the function will have two roots.
Another poster said you could do it using the discriminant, and you could, but this is how you would do it if you don't actually have f(x), and you just have a graph as some questions I've seen. I'll try and find an example and edit this post.

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Hello, would someone help me out in Q9?
http://www.madasmaths.com/archive/iygb_practice_papers/c3_practice_papers/c3_h.pdf
Original post by sabahshahed294


I presume you're fine on the relationship between cot and tan. Use the formula for tan(2theta) to derive a formula for tan(4theta). Then you plug the specific values into everything and the result falls out
Original post by 1 8 13 20 42
I presume you're fine on the relationship between cot and tan. Use the formula for tan(2theta) to derive a formula for tan(4theta). Then you plug the specific values into everything and the result falls out


I'll try giving it a shot. Thank you.
I'm having trouble with question 7:

http://www.madasmaths.com/archive/iygb_practice_papers/c3_practice_papers/c3_u.pdf

I understand that sin-1x = arcsinx but I'm not sure how we can manipulate the equation given. I thought maybe we can take the sin and cosine of both sides simultaneously but I'm pretty sure you can't do that. :colondollar:

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Original post by pineneedles
I'm having trouble with question 7:

http://www.madasmaths.com/archive/iygb_practice_papers/c3_practice_papers/c3_u.pdf

I understand that sin-1x = arcsinx but I'm not sure how we can manipulate the equation given. I thought maybe we can take the sin and cosine of both sides simultaneously but I'm pretty sure you can't do that. :colondollar:

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Not simultaneously - try applying them both to the original to the equation, one at a time.
Original post by SeanFM
Not simultaneously - try applying them both to the original to the equation, one at a time.


Thanks 😊 Im not sure if this is clear enough, not used to working with arcsin etc :
1465678441816.jpg

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