   Chapter 2.1, Problem 2E

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# Graph the curve y = sin x in the viewing rectangles [ − 2 , 2 ] by [ − 2 , 2 ] , [ − 1 , 1 ] by [ − 1 , 1 ] , and [ − 0.5 , 0.5 ] by [ − 0.5 , 0.5 ] . What do you notice about the curve as you zoom in toward the origin?

To determine

To sketch: Graph of the curve y=sinx in the viewing rectangles [-2, 2] by [-2, 2],

[-1, 1] by [-1,1] and [-0.5, 0.5] by [ -0.5, 0.5] and explain what happens when we zoom in the graph towards the origin

Explanation

Graph of the curve y=sinx in the viewing rectangle [-2, 2] by [-2, 2] is

Graph of the curve y=sinx in the viewing rectangle [-1, 1] by [-1, 1] is

Graph of the curve y=sinx in the viewing rectangles [-0.5, 0.5] by [-0.5, 0.5]

From the above graphs we observe that, when we zoom in the graph towards the origin, the graph of y=sinx, starts looking like the graph of the curve y=

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