C2 may be the first “proper” A level Mathematics you do. I’m not saying C1 is easy, but a lot of C1 overlaps with Higher GCSE material. C1 is a lovely overlap between GCSE and new material of A level, so make sure you master it all before moving onto C2.
Guide to C2
I am currently updating this guide for C2, hopefully the areas I have completed below will help…
The trigonometry is split into two parts, the geometry bit (area of sectors and triangles and stuff) and the more pure conceptual bit (solving trigonometric equations). It’s probably best to learn those two bits separately. Both will require you to learn about radians, so we might as well start there.
You need to know what radians are. You don’t need to convert, I never convert, you just do a question in radians or you do it in degrees.
Most geometry questions are in radians, and using them you need to know the area of triangles, sectors and segments. This will require use of the Sine rule and Cosine rule from GCSE. Most of these questions are just manipulating formulae and extracting information. Enough practice and you will master this quickly.
Question 5 on the C2 May 2011 paper has a tricky example of finding the area of shapes made with sectors.
Solving trigonometric equations in C2 can use a variety of techniques and can be in degrees or radians. You have to start by simply being able to solve trigonometric equations such as sinx=0.5. There will be multiple solutions, so you might want to refresh sketching the trig graphs (near the end of this tutorial). After that, you need to learn how to solve trigonometric equations with transformed domains (sin3x=0.5).
Part (a) of question 7 on the C2 May 2011 paper has an example of transformed domains
Next you need to solve trigonometric quadratic equations, to do this, depending on your mastery of other areas, you may need to revise solving quadratics from GCSE/C1, both factorising easy ones, hard ones and using the formula.
Now the most challenging bits of trigonometry involve identities. You don’t need to prove them, but so you know where they come from you should look at the proof that sin²θ + cos²θ = 1 but more importantly use sin²θ + cos²θ = 1 to solve equations.
Part (b) of question 7 on the C2 May 2011 paper has an example of using the sin²θ + cos²θ = 1 identity
Then have a look at the proof that tanθ = sinθ / cosθ and once again use tanθ = sinθ / cosθ trigonometric identity to solve equations.
Part (ii) of question 7 on the C2 January 2009 paper has an example of using the tanθ = sinθ / cosθ identity.
Just a word of warning. Not all equations with multiple ratios (i.e. sine, cosine and/or tangent in the same question) need an identity. If a set of brackets are already factorised you can get answers directly from the brackets.
Part (i) of question 7 on the C2 January 2009 paper has an example of a question that doesn’t need an identity but looks like it does.