Problem

For \(f(x)~=~\sin(x)\) and \(g(x)~=~\tan(x)\), state \(\text{both}~\text{domains}~\text{and}~\text{ranges}\), including the repeated tangent exclusions, then compare each pair using equality or proper-subset relationships.

Sine and tangent graphs from negative pi to pi with tangent gaps at plus or minus pi over 2.

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Domain f=ℝ; range f=ℝ. Domain g excludes π/2+kπ; range g=ℝ. Domain g is a proper subset of domain f, and the ranges are equal.

Domain f=ℝ; range f=[−1,1]. Domain g excludes kπ; range g=[−1,1]. Domain g is a proper subset of domain f, and the ranges are equal.

Domain f excludes π/2+kπ; range f=ℝ. Domain g=ℝ; range g=[−1,1]. Domain f is a proper subset of domain g, while range g is a proper subset of range f.

Domain f=ℝ; range f=[−1,1]. Domain g excludes π/2+kπ for integers k; range g=ℝ. Domain g is a proper subset of domain f, while range f is a proper subset of range g.

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For \(f(x)~=~\sin(x)\) and \(g(x)~=~\tan(x)\), state \(\text{both}~\text{domains}~\text{and}~\text{ranges}\), including the repeated tangent exclusions, then compare each pair using equality or proper-subset relationships.

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