QuestionHere is a little more review concerning trig functions. Using the formula for and of the sum of two angles.
Now reverse this formula and given the expanded version find the version with just one term. This involves solving a pair of equations -in order to get what values must you choose for and ? (Match coefficients.)
By convention we'll assume that the amplitude (the first coefficient on the left hand side) is positive.
The upshot of this exercise is that we can always rewrite the sum of multiples of and as a single function with a given amplitude and phase shift. We could also write it as a single ), but it would have a different phase in that case. We'll use this many times in interpreting results.
Studdy Solution
Solve for using the tangent identity:
The values for and are:
1. For : ,
2. For : ,
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