Problem

Put your calculator in radian mode, and use the viewing window given by 0 ≤ x ≤ 6.28 and −...

Put your calculator in radian mode, and use the viewing window given by 0 ≤ x ≤ 6.28 and −2 ≤ y ≤ 2.*

(a) Graph y = sin x


(b) Graph y = sin (2x)


(c) Graph y = sin (3x)


(d) On the basis of parts (a)–(c), what do you think the graphs of y = sin (4x), y = sin (5x), y = sin (6x), and so on, will look like? Use the calculator to verify your answer.


(e) On the basis of part (d), what do you think the graphs of y = sin (50x) and y = sin (100x) will look like? What does a calculator display instead? What might explain the graphs of the calculator?

*You don’t need to know what radian mode is or what "sin" means. Just use the calculator key with this label.

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