Problem

Identify the basic trigonometric function shown with increasing branches and vertical asymptotes at \(x~=~\pi~/2~+~k\pi~\), and justify the identification from those features.

Answer choices

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It is the sine function because sine is repeating, so the branches and gaps fit its graph pattern.

It is the tangent function because tangent has increasing branches separated by vertical asymptotes at x = pi/2 + kpi.

It is the cosine function because cosine repeats and has turning points, so it matches these graph features.

It is the secant function because secant has vertical asymptotes at x = pi/2 + kpi, so the graph must be secant.

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