Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Decide the sign of sin, cos and tan in each quadrant
Trigonometry
CCSS HSF.TF.A.2England: A-level Pure Mathematics
Objective and success criteria
Students will: Decide the sign of sin, cos and tan in each quadrant.
- 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: The unit circle and radians
Leads to: Use reference angles for angles beyond 90°; Use sin²θ + cos²θ = 1 to find exact values
Materials: Scientific calculators, Protractors and rulers, Right-triangle diagrams, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (The unit circle and radians). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Convert π/3 radians to degrees. → 60Prompt: π radians is a half turn.
- Is sin 0° positive, zero or negative? (Positive / Zero / Negative) → ZeroPrompt: On the unit circle, cos is the x-coordinate and sin is the y-coordinate.
- Convert 2π radians to degrees. → 360Prompt: π radians is a half turn.
Hook · 5 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Decide the sign of sin, cos and tan in each quadrant. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Without a calculator, is sin 108° positive or negative?
- Step 1: 108° is in quadrant 2.
- Step 2: Positive
- Answer: Positive
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Without a calculator, is tan 36° positive or negative? (Positive / Negative) → PositivePrompt: Which quadrant is the angle in?
- θ is in the fourth quadrant. Is tan θ positive or negative? (Positive / Negative) → NegativePrompt: cos is the x-coordinate and sin is the y-coordinate on the unit circle.
You do: independent practice · 10 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 · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Without a calculator, is cos 106° positive or negative? (Positive / Negative) → NegativePrompt: Which quadrant is the angle in?
- θ is in the first quadrant. Is tan θ positive or negative? (Positive / Negative) → PositivePrompt: cos is the x-coordinate and sin is the y-coordinate on the unit circle.
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: The unit circle and radians.
- 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: Use reference angles for angles beyond 90°; Use sin²θ + cos²θ = 1 to find exact values.
- 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