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Basic Phasors and the simple Wave Function

This is an introduction to phasors and their use in representing a sinusoidal wave. Here, after describing their usefulness, they will be used to show how a simple vector diagram can reduce the wave function acosx + bsinx to a single wave ksin(x+a). If you are sitting The SQA higher maths exam, I hope you will be impressed by how simple this technique is. Unfortunately, the SQA only want the longer method of expanding using the addition formulae, equating coefficients, and then solving the simultaneous equations to obtain the results. I would consider the wording of their exam questions inappropriate, as they do not specify a technique, and as such any valid mathematical method could be used to obtain the result. Their wording should be "find algebraically ...", but they only accept the algebraic method in their marking! So don't use this method in their exam! You can quickly check the result of course with a quick thumbnail sketch of the phasors. Certainly use it otherwise, as it is so simple and much more enlightening. I first go through a few examples then give a further two for the viewer to try, followed by the solutions.