1. Mathematical Studies for the IB Diploma © Hodder Education 2010 4.5 General equation of the sine function

2. Mathematical Studies for the IB Diploma © Hodder Education 2010 General equation of the sine function The basic sine function takes the form f(x) = sin x. Its shape for the values of x in the range 0 ≤ x < 360º is as shown below. It has certain properties. – It has a period of 360º (i.e. it repeats every 360º). – It has an amplitude of 1. period = 360º amplitude

3. Mathematical Studies for the IB Diploma © Hodder Education 2010 General equation of the sine function The sine function takes the more general form f(x) = a sin bx + c. The values of a, b and c transform the shape or the position of the graph in different ways. Therefore ‘a’ transforms the graph by stretching it by a scale factor of a parallel to the y-axis. The graph of f(x) = 2 sin x has: a period of 360º an amplitude of 2.

4. Mathematical Studies for the IB Diploma © Hodder Education 2010 General equation of the sine function Therefore ‘b’ transforms the graph by stretching it by a scale factor of parallel to the x-axis. The graph of f(x) = sin 2x has: a period of 180º an amplitude of 1.

5. Mathematical Studies for the IB Diploma © Hodder Education 2010 General equation of the sine function Therefore ‘c’ transforms the graph by translating it by the vector The graph of f(x) = sin x + 1 has: a period of 360º an amplitude of 1.