Math lesson plan · 12th grade (Year 13 in England) · 60 minutes
Solve trigonometric equations
Trigonometry
CCSS HSF.TF.B.7
Objective and success criteria
Students will: Solve trigonometric equations.
- 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; Find angles with inverse trig
Leads to: Solve trigonometric equations between 0° and 360°
Materials: Scientific calculators, Protractors and rulers, Right-triangle diagrams, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (The unit circle and radians; Find angles with inverse trig). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Convert 30° to radians (in terms of π). (π/4 / π/6 / 5π/6 / π/3) → π/6Prompt: A half turn is π radians.
- A right triangle has opposite side 13 cm and adjacent side 7 cm to angle θ. Find θ to 1 decimal place. → 61.7Prompt: Opposite and adjacent: use tan.
- Is cos 120° positive, zero or negative? (Positive / Zero / Negative) → NegativePrompt: On the unit circle, cos is the x-coordinate and sin is the y-coordinate.
Hook · 6 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Solve trigonometric equations. Read the success criteria together.
I do: model it · 12 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°. Give the smaller solution in degrees.
- Step 1: x = 45° or x = 135°
- Answer: 45
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 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.
- Solve tan x = 1 for 0° ≤ x < 360°. Give the larger solution in degrees. → 225Prompt: Find the reference angle from the exact values.
- Solve cos x = √3/2 for 0° ≤ x < 360°. Give the smaller solution in degrees. → 30Prompt: Find the reference angle from the exact values.
You do: independent practice · 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Solve tan x = −1 for 0° ≤ x < 360°. Give the larger solution in degrees. → 315Prompt: Find the reference angle from the exact values.
- Solve sin x = √2/2 for 0° ≤ x < 360°. Give the smaller solution in degrees. → 45Prompt: Find the reference angle from the exact values.
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: Solve trigonometric equations between 0° and 360°.
- 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