Precalculus · Unit 3 · Paper 3

Trigonometric & Polar Functions unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1 Paper 2 Paper 3

Each paper is built from this unit’s 37 terms and is the same for everyone, so a teacher can assign “Unit 3, Paper 3” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.

Suggested time 36 min 33 points0/17 attempted

Finding where a polar curve crosses the origin

Law of cosines

Angular and linear speed

Solving trig equations

Area of a triangle from two sides and the included angle

Sum and difference identities

Rate of change in polar functions

Trig identities as a proof tool

Reciprocal functions

Reference angle

Double angle identities

Signs by quadrant

Short answer 1. Define or explain: Radian measure

3 pts

Short answer 2. Define or explain: Period of a trig function

3 pts

Short answer 3. Define or explain: Even-odd trig identities

3 pts

Short answer 4. Define or explain: Sinusoidal regression vs algebraic fitting

3 pts

Free response

9 pts

The depth of water in a harbor is modeled by d(t) = 4.2 + 2.8·sin(π(t − 3)/6), where d is in meters and t is hours after midnight.

Determine the midline, amplitude and period of the model, and interpret the midline in context.

Determine the maximum depth and the first time after midnight at which it occurs.

A vessel requires at least 5.6 m of water. Determine the first interval after midnight during which the vessel can safely enter, to the nearest hundredth of an hour.

Explain why the model predicts the same depths on the following day, and state one reason the actual depths might differ.