Last edited by InteGrand; 17 Jan 2017 at 6:03 AM.
The inspiration of that question was actually just the fact
a sin(x) + b cos(x) = b cos(x) + a sin(x)
Last edited by davidgoes4wce; 6 Feb 2017 at 2:13 PM.
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- a quick inverse trig question
Q. let f(x) = sin^(-1) (x)
a) for what values of m does the line y = mx cut y = f(x) at three points
b) Investigate the concavity of the curve and find the coordinates of the point of intersection
a)
because is an odd function. So to find all possible lines we have to make sure that it passes through the origin, which it always does, and one point on the first quadrant (x,y). and by oddness of , the line also passes through (-x,-y) as well. therefore
But at x=0 the tangent has a slope of 1 therefore
m > 1
b) Well, just take the second derivative and the intersection points are :
Mahan Ghobadi
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Last edited by Mahan1; 6 Mar 2017 at 7:21 PM.
Mahan Ghobadi
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If you have trouble with Mathematical Induction, can you always expand the equation? It works, but it's just really slow.
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Well just say you're solving an equation and you're at the RTP step.
You have to prove LHS = RHS, which is
k/6 (k+1)(2k+1) + (k+1)^2 = (k+1)/6 (k+2)(2k+3)
Can you simplify and expand left hand side, then simplify and expand the right hand side, so they're equal?
I'm not moving the equation to the other side, but just simplifying it. It works if you can't figure out how to manipulate the factors. Is it possible to do that though?
Prove the following statement using mathematical induction
The last term on the L.H.S has n-digits
Mahan Ghobadi
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Different books do it slightly differently for some reason. I did all of the Year 10 5.3 Questions (Congruency triangles & Circle Geometry) from Cambridge text book and they did it in the a chronological order.
I also had a look at the Oxford textbook and their method of reasoning and the way they write it , I noticed it is slightly different to the Cambridge text.I have a personal preference towards the way they write in Cambridge.
Last edited by davidgoes4wce; 20 Jun 2017 at 3:30 PM.
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I also do notice a huge overlap in 5.3 Maths Year 10 and Year 11 Prelim Extension 1 maths. (Trig, Circle Geometry, Polynomials in particular)
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Consider the five functions:
How many are even functions and how many are odd functions?
I was a bit unsure about ?
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Part ii please
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Last edited by kawaiipotato; 1 Oct 2017 at 6:29 PM.
Sxc avatar made by a sxc person: carrotontheground http://community.boredofstudies.org/...otontheground/
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