Trig Identities: Test, Simplify, Catch the Error

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Mathematics · Precalculus / Trigonometry
SP-PRECAL-003 · Free to print and use in your classroom · substituteplans.com
Page 2
Trig Identities: Test, Simplify, Catch the Error
Mathematics · Precalculus / Trigonometry · Grades 11-12 · 50 minutes
Time needed
50 minutes (one class period)
Prep
Copy the 2-page worksheet (one per student). Write the Pythagorean identity on the board.
Technology
None. Calculators are optional (all decimals needed are printed).
Student
independence
High. Students work alone, then compare with a partner.
Copies to make
One 2-page worksheet per student
Materials
Pencils, Worksheet, Whiteboard or chalkboard
Goal for today: Students will use basic trigonometric identities to find missing values, simplify expressions, and test
whether a claimed identity is false.
Before the bell
☐ Copy the worksheet, one per student (2 pages).
☐ Write on the board: sin²x + cos²x = 1 and tan x = sin x / cos x.
☐ Keep the answer key on your desk. You do not need to solve anything yourself.
Say this to start
Good morning! Today in trigonometry you will work with identities, which are equations that are always true. You will
test claims with numbers, use the Identity Toolbox to simplify expressions, and catch a common algebra mistake. The
toolbox at the top of the worksheet has every rule you need. Please work on your own, and 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 two
identities on the board.
Settle in and read the Identity Toolbox.
5–10
Read this example aloud: if sin θ = 3/5 in Quadrant I, then
cos² θ = 1 − 9/25 = 16/25, so cos θ = 4/5.
Follow along and ask questions about the
example.
10–20
Students complete the Part A table. Tell them one
counterexample is enough to show a claim is not an
identity.
Compute both sides at 30° and decide.
20–32
Students do Part B (questions 1–3). Walk the room and ask,
“Which quadrant? Is the answer positive or negative
there?”
Find missing trig values and show the work.
32–44
Students do Part C (questions 4–8), Part D (questions 9–11)
and Part E (question 12).
Simplify, choose answers, and explain the
algebra mistake.
44–50
Read answers to questions 1–11 from the key. Students
mark their work. Collect worksheets.
Check answers and hand in the worksheet.

SubstitutePlans.com
Mathematics · Precalculus / Trigonometry
SP-PRECAL-003 · Free to print and use in your classroom · substituteplans.com
Page 3
If things go wrong
• If students say they have not seen identities before, point them to the toolbox and the worked example; most
items need only one or two rules.
• If students are stuck on Part C, suggest rewriting everything in terms of sine and cosine first.
• If a student gets a sign wrong in Part B, ask which quadrant the angle is in and which functions are positive
there.
• If a student finishes early, use the early finisher list.
Early finishers
• Show that 1 + cot²x = csc²x by dividing sin²x + cos²x = 1 by sin²x.
• Test the claim cos(2x) = 2 cos x at x = 60° and decide if it is an identity.
Support and challenge
• Support: Students complete Part A, questions 1, 4, 5 and 9, and the example from Part E.
• Challenge: Ask students to prove tan x + cot x = sec x csc x, starting from the left side.
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: