Before You Start

Solving a trig. equation can be difficult at times, knowing what method to use. I have tried to break these steps down into some kind of order. Also make sure you are familiar with the quadrant rule before you start. I find this makes solutions easier than using a graphical method.

Solving Trig Equations

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.

 

Worked Solutions to (1), (2) and (3)

Numerical Answers Only

 

Can it be written in the same trig. function when the angles are the same?

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.

The examples are:

Worked Solutions to (4), (5) and (6)

Numerical Answers Only

 

When the angles are different. Is One angle Double the Other?

More identities involving the use of the double angle formulae may be useful in cases where one angle is double another.

 

Here are examples that use these identities. You will see that one angle is double another.

Worked Solutions to (7), (8) and (9)

Numerical Answers Only

Is the equation of the form A sin x ± B cos x

or A cos x ± B sin x ?

These identities are useful when solving equations with the following forms.

Proofs of these identities

In the examples that follow, I show you how to use them to change the equation into one with one trig. function.

Worked Solutions to (10) and (11)

Numerical Answers Only

 

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