Family Overview

In Plain Language

Topic 3.5 names the key characteristics of sine and cosine as sinusoidal functions.

• Sinusoidal: any function built from additive and multiplicative transformations of $y=\sin\theta$ (sine and cosine themselves count) (3.5.A.1).
• Period & frequency: reciprocals; for $y=\sin\theta$ and $y=\cos\theta$, period $2\pi$ and frequency $1/(2\pi)$ (3.5.A.2).
• Amplitude: half the gap between max and min; for parent sine/cosine, amplitude $1$ (3.5.A.3).
• Midline: average of max and min; for parents, $y=0$ (3.5.A.4).
• Concavity: as inputs increase, the graph switches between concave down and concave up (3.5.A.5).
• Symmetry: $y=\sin\theta$ is odd; $y=\cos\theta$ is even (3.5.A.6).

Why It Matters

These vocabulary pieces (amplitude, period, midline, frequency, odd/even) are the language of every later sinusoidal model and FRQ. Topic 3.6 then layers full transformations on this foundation.

How Families Can Help

• From a wave sketch: find max, min, midline, amplitude, and one period length.
• Ask: "Is this odd or even?" for parent sine vs cosine.
• Practice: frequency $=1/$period.

What Not to Do

• Do not confuse amplitude with the maximum value when the midline is not zero.
• Do not swap period and frequency.
• Do not call cosine odd or sine even.