Find A, B, C, and if 40 cos(100t 40) 20 sin(100t + 170) = A cos 100t + B sin 100t = C

Chapter 10, Problem 10.2

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QUESTION:

Find A, B, C, and \(\phi\) if \(40\ cos (110t - 40^{\circ}) - 20\ sin (100t + 170^{\circ}) = A\ cos\ 100t + B\ sin\ 100t = C\ cos(100t + \phi)\).

Questions & Answers

QUESTION:

Find A, B, C, and \(\phi\) if \(40\ cos (110t - 40^{\circ}) - 20\ sin (100t + 170^{\circ}) = A\ cos\ 100t + B\ sin\ 100t = C\ cos(100t + \phi)\).

ANSWER:

Step 1 of 7

Consider the equation;

.......(1)

Using the trigonometric formulae

                                        

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