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MATH 1211 Calculus Discussion Forum Unit 1. University of the People (Uopeople). Bachelor of Science
Typology: Assignments
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1. Considering the graph of the function y = sin x + cos x, its overall shape is described below:
Is it periodic?
Yes, the graph is periodic.
How do you know?
This is periodic because the function from the graph has a repeating pattern. It does have amplitude and restarts after a duration of 2 pi cycles.
2. Using a graphing calculator or other graphing devices, estimate the x- and y-values of the maximum point for the graph (the first such point where x > 0). It may be helpful to express the x-value as a multiple of π.
The period of x is 2 pi and the value of y is 1.414 units, therefore y = 1.414 and x = 2 pi.
3. Now consider other graphs of the form y = A sin x + B cos x for various values of A and B.
Sketch the graph when A = 2 and B = 1, and, find the x - and y-values for the maximum point. (Remember to express the x-value as a multiple of π, if possible.)
