Math lesson plan Β· 11th grade (Year 12 in England) Β· 60 minutes
Use reference angles for angles beyond 90Β°
Trigonometry
CCSS HSF.TF.A.2England: A-level Pure Mathematics
Objective and success criteria
Students will: Use reference angles for angles beyond 90Β°.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Decide the sign of sin, cos and tan in each quadrant
Leads to: Solve trigonometric equations between 0Β° and 360Β°
Materials: Scientific calculators, Protractors and rulers, Right-triangle diagrams, Mini whiteboards and pens, Printed student sheet (below).
Warm-up Β· 6 min
- Quick retrieval from earlier learning (Decide the sign of sin, cos and tan in each quadrant). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Without a calculator, is sin 250Β° positive or negative? (Positive / Negative) β NegativePrompt: Which quadrant is the angle in?
- ΞΈ is in the second quadrant. Is sin ΞΈ positive or negative? (Positive / Negative) β PositivePrompt: cos is the x-coordinate and sin is the y-coordinate on the unit circle.
- Without a calculator, is cos 354Β° positive or negative? (Positive / Negative) β PositivePrompt: Which quadrant is the angle in?
Hook Β· 6 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Use reference angles for angles beyond 90Β°. Read the success criteria together.
I do: model it Β· 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: What is the reference angle for 320Β°?
- Step 1: 360Β° β 320Β° = 40Β°
- Answer: 40
- Pause after each step and ask a student to say what comes next.
We do: guided practice Β· 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- What is the reference angle for 189Β°? β 9Prompt: The reference angle is the acute angle between the terminal side and the x-axis.
- Find the exact value of cos 330Β°. (β1/2 / ββ2/2 / 1/2 / β3/2) β β3/2Prompt: Find the reference angle (the acute angle to the x-axis).
You do: independent practice Β· 17 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket Β· 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Find the exact value of sin 300Β°. (β1/2 / ββ3/2 / β2/2 / ββ2/2) β ββ3/2Prompt: Find the reference angle (the acute angle to the x-axis).
- What is the reference angle for 337Β°? β 23Prompt: The reference angle is the acute angle between the terminal side and the x-axis.
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: Decide the sign of sin, cos and tan in each quadrant.
- Use concrete materials: scientific calculators.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Move on to: Solve trigonometric equations between 0Β° and 360Β°.
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-11.
Free lesson plan from eurekami.com/lesson-plan-builder