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 87 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 33 min 30 points0/17 attempted

Signs by quadrant

Amplitude is never negative

Endpoint values give one solution

Angular speed on a rigid body

Factoring before reading a phase shift

Asymptotes of cosecant

Restricted domain of cosine

Polar coordinates

Choosing a cos 2A form

Law of sines

sin(A+B) is not sin A + sin B

No-triangle case in SSA

Short answer 1. Define or explain: Common polar graphs

3 pts

Short answer 2. Define or explain: Stretching the interval for sin(bx)

3 pts

Short answer 3. Define or explain: Solving an equation with sin x and sin 2x

3 pts

Short answer 4. Define or explain: Symmetry of polar graphs

3 pts

Free response

6 pts

NO CALCULATOR IS ALLOWED FOR THIS QUESTION. A rider boards a Ferris wheel at its lowest point at time t = 0. The rider's height above the ground, in meters, is modeled by h(t) = 12 − 10cos(πt/5) where t is measured in minutes.

A. Identify the amplitude, the midline, and the period of h, and state the rider’s minimum and maximum heights above the ground.

B. Find all values of t in the interval 0 ≤ t ≤ 10 for which h(t) = 17. Give exact values.

C. Determine the interval within 0 ≤ t ≤ 10 on which h is increasing, and explain what this represents about the rider’s motion.