Sine and Cosine Graphs: Amplitude, Period, Midline

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Mathematics · Precalculus / Trigonometry
SP-PRECAL-002 · Free to print and use in your classroom · substituteplans.com
Page 2
Sine and Cosine Graphs: Amplitude, Period,
Midline
Mathematics · Precalculus / Trigonometry · Grades 10-12 · 50 minutes
Time needed
50 minutes (one class period)
Prep
Copy the 2-page worksheet (one per student). Write the five graph-formula lines on the board
(see below).
Technology
None. Calculators are optional.
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 determine amplitude, period, midline, maximum and minimum from equations of sine
and cosine functions and write equations from descriptions.
Before the bell
☐ Copy the worksheet, one per student (2 pages).
☐ Write on the board: Amplitude = |A|. Period = 2π/B. Midline: y = D. Max = D + |A|. Min = D − |A|.
☐ Keep the answer key on your desk. You do not need to graph anything yourself.
Say this to start
Good morning! Today's math is about the graphs of sine and cosine waves. Each wave has a height, a length and a
center line. The formulas are on the board and on the top of the worksheet, so you can read the numbers right out of
the equations. Please work quietly 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. Point to the
formulas on the board.
Settle in and read the directions at the top
of the page.
5–10
Read this example aloud: y = 2 cos(3x) + 1. Amplitude 2,
period 2π/3, midline y = 1, max 3, min −1.
Follow along and check the example
against the formulas.
10–22
Students complete the Part A table. Walk the room and
ask, “What is A? What is B? What is D?”
Read A, B and D from each equation and fill
in the six columns.
22–30
Students complete the Part B table of values for y = 2 sin x
+ 1.
Substitute each x-value and write the
y-value.
30–42
Students do Part C (questions 1–3), Part D (questions 4–7)
and Part E (questions 8–10).
Write equations from descriptions, answer
multiple choice, and decide true or false.
42–50
Read answers to questions 4–10 from the key. Students
mark their work. Collect worksheets.
Check answers and hand in the worksheet.

SubstitutePlans.com
Mathematics · Precalculus / Trigonometry
SP-PRECAL-002 · Free to print and use in your classroom · substituteplans.com
Page 3
If things go wrong
• If students ask about the period of a function with B, point them to the formula on the board: period = 2π
divided by B.
• If students are unsure whether the negative changes amplitude, tell them amplitude is always positive; the
negative only flips the graph.
• If the table in Part B confuses them, tell them to substitute x into 2 sin x + 1 and use the sine values printed
above the table.
• If a student finishes early, use the early finisher list.
Early finishers
• Sketch one full cycle of y = 2 sin x + 1 on the back of the worksheet using the Part B points.
• Make up an equation with amplitude 3, period 6π and midline y = −1, then trade with a partner to check.
Support and challenge
• Support: Students complete Part A rows 1, 2 and 5, Part B, and questions 4, 5 and 8.
• Challenge: Ask students to write an equation for a wave with max 9, min −3 and period 10, and explain how
they found each number.
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: