Problem

Use the graph of \(y~=~\sin(x)\) on \([0,~2\pi~]\) to state the domain, complete-cycle count, amplitude, period, midline, range, and all zeros, maxima, and minima on the interval.

Exact sin curve on [0,2π] with radian axes and all key locations visible but unlabeled.

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What this problem is really about

Read one sine cycle through its five quarter-period anchors: midline, maximum, midline, minimum, midline. Those anchors organize the period, amplitude, range, zeros, and extrema at once. Because the interval is closed, inspect both endpoints before declaring any feature list complete.

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The domain is [0, 2pi]; there are 1 complete cycle(s), amplitude 1, period 2pi, midline y = 0, and range [-1, 1]. Zeros are (0,0), (pi,0), (2pi,0); maxima are (pi/2,1); minima are (3pi/2,-1).

The domain is [0, 2pi]; there are 1 complete cycle(s), amplitude 1, period 2pi, midline x = 0, and range [-1, 1]. Zeros are (0,0), (pi,0), (2pi,0); maxima are (pi/2,1); minima are (3pi/2,-1).

The domain is [0, 2pi]; there are 1 complete cycle(s), amplitude 1, period pi, midline y = 0, and range [-1, 1]. Zeros are (0,0), (pi,0), (2pi,0); maxima are (pi/2,1); minima are (3pi/2,-1).

The domain is [0, 2pi]; there are 1 complete cycle(s), amplitude 2, period 2pi, midline y = 0, and range [-1, 1]. Zeros are (0,0), (pi,0), (2pi,0); maxima are (pi/2,1); minima are (3pi/2,-1).

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Use the graph of \(y~=~\sin(x)\) on \([0,~2\pi~]\) to state the domain, complete-cycle count, amplitude, period, midline, range, and all zeros, maxima, and minima on the interval.

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