Edexcel Core 2 : Trigonometry - Equations, Identities
Overview
In this revision guide I have tried to breakdown what you need to look for when solving a basic trig. equation.
You generally need to get the equation into one trig. function and / or see if it factorises when equal to zero.
Past Paper Exam Questions
All the questions on trig. equations come with video worked solutions to help you with your maths revision.
Edexcel C2 June 2006, Question 6
Edexcel C2 January 2007, Question 6
Edexcel C2 January 2008, Question 4
Edexcel C2 June 2008, Question 9
Edexcel C2 January 2009, Question 8
Edexcel C2 June 2009, Question 7
Edexcel C2 January 2010, Question 2
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Revision Guide
The Quadrant Rule
The quadrant rule is very useful to know as it saves you having to draw graphs to find a set of solutions in a given range. I would strongly recommend that you learn this method.
Using the Quadrant Rule
In the following examples I show how the quadrant rule is used to find a set of solutions in a given range. There are 6 possibilities where sin is positive or negative, and the same for cos and tan functions.
I would encourage you to learn these methods as you will need top use them in the endings to more complex equations and so this is essential knowledge.
- How to solve sin θ = positive value
- How to solve sin θ = negative value
- How to solve cos θ = positive value
- How to solve cos θ = negative value
- How to solve tan θ = positive value
- How to solve tan θ = negative value
You will then need to be able to solve equations with multiple angles.
Such as
Try it first then check with the worked solution
Hopefully now you should be able to use the quadrant rule to find angles in a given range.
Moving on to more involed Trig. Equations
Once you have grasped the quadrant rule it is time to move on and solve more involved equations.
You should have a stratedgy for solving trig. equations.
Always ask yourself - Does it factorise when equal to 0?
- If it does then quite often each factor can be solved as an equation in its own right as in these examples.
See the Video Worked Solutions to (1), (2) and (3)
And ask yourself - Can it be written in the same trig. function?
You may need to use an identity to write an equation in the same trig. function which may then possibly factorise.
In these examples I show you how the identities
can be used to solve equations with different trig. squared functions in. You need to learn these.
The examples are:
See the Video Worked Solutions to (4), (5) (6) and (7)
Proving Trig. Identities
You will be expected to be able to prove a trig. identity such as the example below. In the video I show you how to set out an identity and what to look for.
This is a tricky topic and one that I find students give in too quickly. Learn your formulae and have patience.
In each of the examples below I aim to demonstrate various common methods. (especially in 2). I would encourage you to try them first before loolking at the worked solution.
