A level revision

Solution of trigonometric equations

To help solve trigonometric equations you need to be able to simplify certain expressions using the following two general expressions:

Where , and

Using these expressions

To simplify expressions

The first thing you need to be able to do with these expressions is use them to simplify longer expressions.

Example question: Show that may be written as

Worked solution: This looks rather nasty, but it is pretty easy if you take it step by step. Firstly equate with , from above:

Now using the above expression for r, substitute in the values of a = 4 and b = 5:

Now we can find :

Therefore the final solution is:

As we were asked to show.

Finding the minimum and maximum values

The minimum and maximum values are given by the coefficient of the sin or cos function, in the above example they are and

Drawing graphs

You need to be able to draw graphs of equations in the form and . This done by starting with a graph of or and translating it by and stretching it by a factor of r parallel to the y axis.

Solving equations

You may be asked to solve something like . First step is to collect like terms on either side to leave you with . From here let x = and solve . This gives you the values that x = 30 or x = 150. Substituting these values of x back into the equation in the previous step:

 or 

Allows you to find the values of as 120 or 240.