Back to Explain symmetry and periodicity — Problem 2 · Task Set 69

HSF.TF.A.4 Tutor Intake — Symmetry and Periodicity of Trig Functions

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Grade 9·11 problems·~14 min·Common Core Math - HS Functions·group·hsf-tf-a-4

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Concepts

Using the same unit-circle reflection (angle $x$ at $(a, b)$ , angle $-x$ at $(a, -b)$ ),
what does this tell us about sine?

Sine is even because both points share the x-coordinate $a$ .

Sine is odd because $\sin(-x) = -b = -\sin(x)$ ; the y-coordinates are opposites.

Sine is odd because sine values are negative for negative angles.

Sine is even because $\sin(-x) = b = \sin(x)$ ; the y-coordinate is unchanged.