Problem

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

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

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What this problem is really about

Cosine uses the same quarter-period spacing as sine but begins at a maximum: maximum, zero, minimum, zero, maximum. From that pattern, read the vertical structure, period, and all special points, including extrema at closed endpoints. Its reflection symmetry about the vertical axis supplies the parity check.

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

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

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

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

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

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