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If you can sketch the graph of y = f(x) = cos(theta), then the graph of y = g(x) = cos(2*theta) is just obtained by contracting the graph of y = f(x) horizontally by a factor of 2.

Try sketching the graph of the function and figure it out from that.

The symbols – and \ are both commonly used for set difference.

That's a bit risky to say, e.g. Im(i) = 1 is true. When we flip i to -i, we get Im(-i) = 1, which is false.

In your question, the two great circles have angle between them theta and meet at antipodal points P, P'. To visualise this, take one great circle to be the equator, and imagine the second one as follows: start with a second equator identical in location to the first, and just "tilt" this up the...

You can find pictures of spherical triangles here: https://en.wikipedia.org/wiki/Spherical_trigonometry. Also here: https://en.wikipedia.org/wiki/Spherical_geometry.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread From isosceles triangle AED, ABC, etc., we get that their base angles are 36 deg, because they have an angle of 108 deg (the pentagon's interior angle) and the angle sum of a triangle is 180 deg. So angle CAB = 36 deg, i.e...

Most HSC maths things are 'assumed because they sound right', e.g. limits, integration, volumes, etc.

Yeah I remember something similar in an old BOS thread too.

I'm not sure it's worth the risk though, at least internally. There was an old BOS thread where someone used matrices to find a triangle area for fun (just to see if he'd get the marks, I think it was a 2U assessment and he was planning to do 4U or something like that) and he got given 0 with...

Are you sure you're allowed to use matrices for the Conics section in HSC? Because that'll really trivialise some of the questions they ask.

Well found that post here: So he/she was doing it just to test our knowledge and improve his/hers.

I thought eyeseeyou was just asking "why" repeatedly as a joke (initially I thought it was serious, but after a while it seemed like a joke). Like he/she asked in another thread I think whether we minded his/her asking why to 'annoy' us or something like that. That post made it seem like he/she...

Yeah, a graphical approach was my first thought for Q3.

theta = 45 deg, 225 deg.

Since we are only after relative incomes, we can set the income of A to be 1 (in unit of currency), then find B and C's incomes; these'll be ratios of that of A. Let the income of B be b and C be c (these are relative to A's income). From info regarding things bought from A, we have: 3/4 +...

Why? (:p)

ΣF stands for the sum of all forces, which is by definition the net force (which is also what the "F" in "F = ma" stands for).

You can see the derivation of Coulomb's Law from the integral form of Gauss's Law here: http://physics.stackexchange.com/questions/44418/are-the-maxwells-equations-enough-to-derive-the-law-of-coulomb .

Yeah, the BCS theory as taught in HSC Physics is actually wrong.