Trigonometric functions – Grade 12 math lesson
Lesson 4 of 5 in the Grade 12 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 12 (ages 17–18) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 12 (ages 17–18)
- You need
- Paper, a pencil and this page
- Graded
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Why do sine and cosine graphs repeat?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Mixing up degrees and radians on a calculator. Check the mode before you start.
- Thinking sin θ can be bigger than 1. On the unit circle the y-value is never more than 1.
Tip for home: Look at tides or daylight hours: they rise and fall like a sine curve.
What your child will learn
Learning goal: use radians, the unit circle and the graphs of sine, cosine and tangent.
Success looks like
- I can convert between degrees and radians.
- I can use the unit circle.
- I can describe trig graphs.
Key words
- radian
- the angle made by an arc as long as the radius
- unit circle
- a circle of radius 1 centered at the origin
- period
- the length of one repeat of the graph
- amplitude
- the height of the wave from its middle
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Mark angles on a large circle in both degrees and radians.
The big ideas (for the adult)
Radians measure angles by arc length: a full turn is 2π radians, so π radians = 180°.
On the unit circle, the point at angle θ is (cos θ, sin θ). This defines sine and cosine for any angle.
Sine and cosine graphs repeat every 2π (their period) and stay between −1 and 1 (amplitude 1). Use symmetry to find related angles.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.
More practice
More Grade 12 math lessons
Curriculum
Common Core State Standards HSF.TF.B.6: “(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.”
Common Core State Standards HSF.TF.B.7: “(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.*”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.