Unit Circle Special Angles: Fill, Convert, Match

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Mathematics · Precalculus / Trigonometry
SP-PRECAL-001 · Free to print and use in your classroom · substituteplans.com
Page 2
Unit Circle Special Angles: Fill, Convert, Match
Mathematics · Precalculus / Trigonometry · Grades 10-12 · 50 minutes
Time needed
50 minutes (one class period)
Prep
Copy the 2-page worksheet (one per student). Nothing else to prepare.
Technology
None. Calculators are not needed (and not helpful) for this lesson.
Student
independence
High. Students work alone, then check with a partner.
Copies to make
One 2-page worksheet per student
Materials
Pencils, Worksheet
Goal for today: Students will find exact sine, cosine and tangent values for special angles and convert between
degrees and radians.
Before the bell
☐ Copy the worksheet, one per student (2 pages).
☐ Write on the board: Cosine = x-coordinate. Sine = y-coordinate. Tangent = sine ÷ cosine.
☐ Keep the answer key on your desk. You do not need to solve anything yourself.
Say this to start
Good morning! Today is a trigonometry practice day. Your teacher wants you to work with the unit circle: fill in a table
of exact values, convert between degrees and radians, and match expressions to answers. The Memory Pattern box on
page 1 has everything you need to start. Work on your own first, and then we will check answers together.

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Mathematics · Precalculus / Trigonometry
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Page 3
Run of show
Minutes
What you do
What students do
0–5
Take attendance. Hand out the worksheet. Write the three
board reminders (cosine = x, sine = y, tangent = sine ÷
cosine).
Settle in and read the directions.
5–10
Ask students to read the Memory Pattern box silently. Then
say: “The sine list goes 0, 1/2, √2/2, √3/2, 1. Cosine is the
same list backwards.”
Read the box and underline the sine
pattern.
10–25
Tell students to complete the Part A table. Walk the room.
If someone is stuck, ask, “Which quadrant is this angle in,
and what is its reference angle?”
Fill in every blank in the table using the
pattern and the sign rules.
25–32
Students do the Part B matching (questions 1–5). Tell them
to use the table they just built.
Match each expression to its exact value.
32–42
Students do Part C conversions (questions 6–11) and Part D
(questions 12–15). Remind them: degrees to radians
multiplies by π/180.
Convert six angles, simplify the fractions,
and choose exact values.
42–45
Students answer the Part E explanation (question 16).
Explain in writing why tan 90° is undefined.
45–50
Read the answers to questions 1–15 from the key. Students
mark their work. Collect all worksheets.
Check answers, fix mistakes, and hand in
the worksheet.
If things go wrong
• If students say they have not memorized the unit circle, point them to the Memory Pattern box. The sine list
and the sign rules let them build every answer.
• If a student gets decimals instead of exact values, remind them the directions ask for answers like √3/2.
• If a student finishes early, check that the table is complete and use the early finisher list.
• If the room gets noisy, remind students this is quiet individual practice until the checking time.
Early finishers
• Add the angles 210°, 225°, 240°, 270°, 300°, 315° and 330° to the table margin with their cosine and sine
values.
• Write a short tip you could give a friend for remembering which quadrants have positive sine.
Support and challenge
• Support: Students complete Part A and questions 1–3, 6 and 12 only.
• Challenge: Ask students to find sin(−π/3) and cos(11π/6) and explain how they decided.

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Mathematics · Precalculus / Trigonometry
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Page 4
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: