Math lesson plan · 12th grade (Year 13 in England) · 30 minutes
Solve trigonometric equations between 0° and 360°
Trigonometry
CCSS HSF.TF.B.7England: A-level Pure Mathematics
Objective and success criteria
Students will: Solve trigonometric equations between 0° and 360°.
- 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: Use reference angles for angles beyond 90°; Solve trigonometric equations
Leads to: the next skill in this area.
Materials: Scientific calculators, Protractors and rulers, Right-triangle diagrams, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Use reference angles for angles beyond 90°; Solve trigonometric equations). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is the reference angle for 319°? → 41Prompt: The reference angle is the acute angle between the terminal side and the x-axis.
- Solve cos x = 1/2 for 0° ≤ x < 360°. Give the smaller solution in degrees. → 60Prompt: Find the reference angle from the exact values.
- Find the exact value of cos 135°. (√3/2 / 1/2 / −1/2 / −√2/2) → −√2/2Prompt: Find the reference angle (the acute angle to the x-axis).
Hook · 3 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Solve trigonometric equations between 0° and 360°. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Solve sin x = −√2/2 for 0° ≤ x < 360°.
- Step 1: Reference angle 45°
- Step 2: 225°, 315°
- Answer: 225°, 315°
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Solve sin x = 1/2 for 0° ≤ x < 360°. (210°, 330° / 150°, 210° / 30°, 150° / 30°, 330°) → 30°, 150°Prompt: Find the reference angle from the exact value.
- Solve sin x = 0.8, giving the solution between 90° and 180° to 1 decimal place. → 126.9Prompt: Your calculator gives the acute solution.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Solve sin x = 0.1, giving the solution between 90° and 180° to 1 decimal place. → 174.3Prompt: Your calculator gives the acute solution.
- Solve cos x = −√2/2 for 0° ≤ x < 360°. (45°, 225° / 135°, 225° / 45°, 135° / 45°, 315°) → 135°, 225°Prompt: Find the reference angle from the exact value.
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: Use reference angles for angles beyond 90°.
- 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
- 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-12.
Free lesson plan from eurekami.com/lesson-plan-builder