Identify the basic trigonometric function shown as a smooth wave with a maximum at \(x~=~0\), and justify the identification from that feature.

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It is the tangent function because trig graphs often begin at x=0, so tangent is the best match.

It is the cosine function because a smooth wave that starts at its maximum when x=0 matches cos(0)=1.

It is the sine function because sine is also a smooth wave, so it fits the description.

It is the sine function because sine and cosine are the same wave, so starting at a maximum does not matter.

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Curriculum context

Course: Math III
Standard: F-TF.2.1
Category: Functions
Domain: Trigonometric Functions
Objective: Graph all six basic trigonometric functions.
Problem type: Identify a basic trigonometric function from its graph features