Common Mistakes
Pre-calculus · AP · Trigonometric and Polar Functions
Focus
Sine and Cosine Function Values
This topic is assessed on the AP Exam.
Frequent mistakes
### 1. Angle mode error
What it looks/sounds like: Calculator is in degrees when radians are required (or vice versa).
Why it happens: Mode is not checked at the start.
How to fix: Write ‘degrees’ or ‘radians’ on the page before evaluating.
### 2. Period/amplitude mix-up
What it looks/sounds like: Horizontal shrink is confused with vertical stretch.
Why it happens: Coefficients on x and y are not separated.
How to fix: Identify b for period and a for amplitude before graphing.
### 3. Correct work, wrong question
What it looks/sounds like: The algebra is fine but answers a different quantity than the stem asks for.
Why it happens: Attention locks onto the first operation instead of the final ask.
How to fix: Underline the final question; after solving, verify the boxed answer matches it.
### 4. Notation and justification gaps
What it looks/sounds like: Missing units, limit language, or ‘because’ statements AP graders expect.
Why it happens: Notation is treated as decoration rather than part of the score.
How to fix: Add one justification phrase per major step (definition, theorem, or rule).
How to avoid them
1. Sketch one period by hand before using technology. 2. Use exact unit-circle values when the exam expects radicals. 3. Label amplitude, period, and phase on graphs.
Quick self-check
- [ ] Can find one exact trig value
- [ ] Can read period/amplitude from an equation
- [ ] Can catch a mode error quickly