Common Mistakes
Trigonometry · Honors Math · Applications of trigonometry
Real mistakes students make on operate on vectors in the plane—and how to catch and fix them.
Focus for this topic: Add, subtract, and scale vectors in the coordinate plane.
Frequent mistakes
### 1. Wrong calculator mode
What it looks/sounds like: Evaluating trig in DEG when the problem is in radians (or reverse).
Why it happens: Mode is invisible until the answer is nonsense.
How to fix: Check DEG/RAD before every evaluation; match the problem’s angle unit.
### 2. Period formula mistakes
What it looks/sounds like: Using 2π/|B| incorrectly or forgetting absolute value.
Why it happens: Students memorize fragments of y = A sin(Bx − C) + D.
How to fix: Write period = 2π/|B| (or 360°/|B|) and compute B from the equation first.
### 3. Phase shift vs vertical shift
What it looks/sounds like: Moving the graph up/down when a horizontal shift was intended.
Why it happens: C and D roles get swapped.
How to fix: Horizontal: solve Bx − C = 0 for the shift; vertical: look at + D.
### 4. Law of Sines/Cosines in the wrong case
What it looks/sounds like: Using the wrong law for AAS vs SAS vs SSS.
Why it happens: Ambiguous SSA is especially easy to mishandle.
How to fix: Classify given parts (AAS/ASA/SAS/SSS/SSA) before choosing a law.
### 5. Identity verification that assumes the result
What it looks/sounds like: Starting from both sides equal instead of transforming one side.
Why it happens: Students work “both ways” until it looks true.
How to fix: Pick one side; rewrite with known identities until it matches the other.
How to avoid them
1. Restate what 4.8 asks in one sentence before computing. 2. Name the method or representation you will use. 3. Define variables with units before writing symbols. 4. Check one easy special case, diagram estimate, or unit/domain check after a long solution. 5. Ask: does this answer match the required form and the prompt?
Quick self-check
- [ ] I can name two mistakes for 4.8
- [ ] I can explain why one of those mistakes happens
- [ ] I can fix one wrong solution by naming the broken step
- [ ] I can check that my final form matches what the prompt asked
Related materials
- Parent Guide, Exam Strategy, and Study Guide for 4.8 (same folder)
- Review and practice-test tiers under this topic when present