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Problem 522
522
The diagram shows part of the graph of \(y = a + b \sin x\). Find the values of the constants \(a\) and \(b\).
Solution
The graph of \(y = a + b \sin x\) is shown with a maximum value of 1 and a mid value of -2, which indicates \(a = -2\).
The amplitude \(b\) is the distance from the midline to the maximum or minimum. Since the maximum is 1 and the midline is -2, the amplitude is \(1 - (-2) = 3\).