Common Mistakes

Frequent Errors

1. Writing $P=(\cos\theta,\sin\theta)$ when radius is not 1. 2. Using QI signs in QII–QIV. 3. Swapping $\sin(\pi/6)=1/2$ with $\sin(\pi/3)=\sqrt{3}/2$. 4. Treating $5\pi/4$ like $\pi/4$ without QIII negatives. 5. Leaving answers as decimals when exact values are required. 6. Wrong reference angle for $7\pi/6$, $5\pi/6$, etc. 7. Multiplying only one coordinate by $r$. 8. Forgetting axis exact values ($0,\pm 1$).

Why These Happen

Students memorize a unit-circle poster and forget the CED scaling $P=(r\cos\theta, r\sin\theta)$ and the "attend to signs" requirement in 3.3.A.2.

How to Fix Them

• Always write the formula with $r$ first.
• Say: "absolute value from triangle; sign from quadrant."
• Check: does $|\sin|$ and $|\cos|$ match the special angle?

Avoidance Scripts

• "$P=(r\cos\theta,\, r\sin\theta)$."
• "Special triangle, then signs."
• "$\pi/6$ vs $\pi/3$: sine is the smaller ratio at $\pi/6$."

Quick Self-Check

• Is $r$ in both coordinates when required?
• Are quadrant signs correct?
• Are $\pi/6$ and $\pi/3$ values not swapped?