Problem

Use the parent \(\text{cosine}\) graph to state its real domain, any excluded inputs, the reason for those exclusions or their absence, and its range as a separate set.

Exact cosine graph over representative cycles with extrema visible; domain and range conclusions are withheld.

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Its domain is all real numbers; excluded inputs are none; the reason is that there is no denominator; and its range is [-1, 1].

Its domain is all real numbers; excluded inputs are none; the reason is that every trig function is defined everywhere; and its range is all real numbers.

Its domain is [-1, 1]; excluded inputs are none; the reason is that cosine is bounded; and its range is all real numbers.

Its domain is all real numbers except 90 + 180k, for integer k; excluded inputs are 90 + 180k; the reason is a zero denominator; and its range is [-1, 1].

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Use the parent \(\text{cosine}\) graph to state its real domain, any excluded inputs, the reason for those exclusions or their absence, and its range as a separate set.

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