Common Mistakes
Frequent Errors
1. Amplitude $=$ maximum value (ignores midline). 2. Period and frequency treated as equal. 3. Measuring from peak to zero as a full period. 4. Saying cosine is odd / sine is even. 5. Forgetting midline is the average of max and min. 6. Confusing concave up/down regions along the wave. 7. Thinking only untransformed sine counts as sinusoidal (cosine and transforms count too). 8. Using degree period $360$ while the axis is in radians without converting.
Why These Happen
Students memorize posters without the CED definitions: amplitude from max/min, frequency as reciprocal of period, and odd/even from symmetry (3.5.A.2–A.6).
How to Fix Them
- Always write: amplitude $=\frac{1}{2}(\max-\min)$, midline $=\frac{1}{2}(\max+\min)$.
- Say: "frequency $=1/$period."
- Test one point for odd/even: $\sin(-\pi/2)=-1=-\sin(\pi/2)$; $\cos(-\pi/3)=\cos(\pi/3)$.
Avoidance Scripts
- "Half the max–min gap is amplitude."
- "Period and frequency are reciprocals."
- "Sine odd; cosine even."
Quick Self-Check
- Do midline and amplitude match the same max/min?
- Is frequency the reciprocal of my period?
- Did I assign odd/even correctly?