Vectors and Polar Coordinates: Convert and Combine

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Mathematics · Precalculus / Trigonometry
SP-PRECAL-004 · Free to print and use in your classroom · substituteplans.com
Page 2
Vectors and Polar Coordinates: Convert and
Combine
Mathematics · Precalculus / Trigonometry · Grades 11-12 · 50 minutes
Time needed
50 minutes (one class period)
Prep
Copy the 2-page worksheet (one per student).
Technology
Calculators are helpful but optional; useful trig values are printed on the worksheet.
Student
independence
High. Students work alone, then compare answers with a partner.
Copies to make
One 2-page worksheet per student
Materials
Pencils, Worksheet, Calculators (optional)
Goal for today: Students will convert between polar and rectangular coordinates and compute vector magnitude,
sum and components.
Before the bell
☐ Copy the worksheet, one per student (2 pages).
☐ Write on the board: x = r cos θ, y = r sin θ, r = √(x² + y²).
☐ Keep the answer key on your desk. You do not need to solve anything yourself.
Say this to start
Good morning! Today is a practice day on two ways of describing a point or direction: polar coordinates (a distance
and an angle) and vectors (two components). The Formula Box on the worksheet has all the rules and the trig values
you need. Please work on your own, then we will check answers.
Run of show
Minutes
What you do
What students do
0–5
Take attendance. Hand out the worksheet. Write the three
formulas on the board.
Settle in and read the Formula Box.
5–10
Read this example aloud: polar point (2, 90°) has x = 2 cos
90° = 0 and y = 2 sin 90° = 2, so it is the rectangular point
(0, 2).
Follow along.
10–20
Students complete the Part A table. Calculators are fine for
the decimals.
Convert four polar points to rectangular
points.
20–32
Students do Part B (questions 1–3). Remind them to sketch
the point to find the correct quadrant for the angle.
Find r and θ, checking the quadrant.
32–44
Students do Part C (questions 4–7), Part D (questions 8–10)
and Part E (questions 11–13).
Work with vectors, answer multiple choice,
and decide true or false.
44–50
Read answers to questions 4–13 from the key. Students
mark their work. Collect worksheets.
Check answers and hand in the worksheet.

SubstitutePlans.com
Mathematics · Precalculus / Trigonometry
SP-PRECAL-004 · Free to print and use in your classroom · substituteplans.com
Page 3
If things go wrong
• If students do not know polar coordinates, point them to the Formula Box and the example; each problem
uses one formula.
• If a calculator is in radian mode, answers will look wrong. Tell students to switch to degree mode.
• If a student gets the wrong angle for a point in Quadrant II or III, ask them to sketch the point; tan⁻¹ alone
gives only Quadrant I or IV angles.
• If a student finishes early, use the early finisher list.
Early finishers
• Find the magnitude of u + v and compare it with |u| + |v|. Are they equal? Explain.
• Convert the rectangular point (−4, −4) to polar form.
Support and challenge
• Support: Students complete Part A, questions 1, 4, 5 and 8, and the true/false items.
• Challenge: Ask students to find the angle that u = <3, 4> makes with the positive x-axis and the angle of v =
<−1, 2>, then explain which vector points more steeply.
Notes for the teacher (you fill this in)
Jot a few lines before you leave. A full Daily Sub Report is in the free Sub Survival Kit at SubstitutePlans.com.
How far the class got / what to pick up next:
Students who were especially helpful:
Anything the teacher should know: