Back to Extend trigonometric functions using unit circle — Problem 3 · Task Set 65

HSF.TF.A.2 Tutor Intake — Unit Circle and Extended Trig Functions

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Grade 9·11 problems·~14 min·Common Core Math - HS Functions·group·hsf-tf-a-2

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Concepts

A student says, "Sine and cosine are only defined for angles between
$0$ and $2\pi$ ." Which response best corrects this statement?

The student is correct; angles outside $[0, 2\pi)$ are
not standard positions and cannot be evaluated.

The unit circle wraps around continuously, so $\sin$ and $\cos$
are defined for any real number input by identifying the
corresponding point on the circle.

Sine and cosine are defined for angles up to $4\pi$ , since the
unit circle completes two full rotations.

Only negative angles are excluded; all non-negative angles are
valid inputs for sine and cosine.