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Expressing Functions of the Form Acosx+Bsinx Rcos(x+alpha)

Linear combinations of trigonometric formulae are very important: in fact any continuous function can be expressed as a sum of sin and cosine terms under certain conditions. Any function of the formcan be expressed in the formor

C can be found simply in any case:but forthe re are 4 possibilities.

If we are expressingin the formthenie

whereand (1)

andwhereand (2)

If we are expressingin the formthenie

whereand (3)

andwhereand (4)

Example: Expressin the form

In expression (3) it is writtenbut we have to write the answer asIn this casewill be negative and we can use (3) still, but we must also recognise that the

Hencewhereis in rads.

Example: Expressin the form

The sin and cos terms are the other way round from that written in (1). Don't let this confuse you. So that the terms match write the question the other way round:

Hencewhereis in rads.