Exercise 17 Page 511

We want to describe and correct the error in finding the amplitude of a sinusoid with a maximum point at $(2,10)$ and a minimum point at $(4,\text{-}6).$

To begin, recall that the amplitude is half the difference between the maximum and minimum value of a periodic function, such as sine or cosine. Recall that values of a function are $y\text{-}$coordinates of points on the graph. We are given that maximum point is $(2,10)$ and minimum point is $(4,\text{-}6),$ therefore the maximum value of the function is $10$ and minimum value of a function is $\text{-}6.$ To obtain the correct amplitude of the function we need to substitute these values into the formula. Comparing it to the method of finding the amplitude given in the exercise, we can see that in the formula addition was applied instead of subtraction. This is the error that was made. Let's now correct this error by using the correct formula!