Trigonometric functions – Grade 11 math lesson

Lesson 13 of 23 in the Grade 11 math course

US version. US grades, US spelling and dollars ($). · UK Maths Department

A complete 45-minute lesson for grade 11 (ages 16–17) 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 11 (ages 16–17)
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

45 minutes in 5 parts
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

All Grade 11 math lessons and tests · Math Department

Curriculum

Common Core State Standards HSF.TF.A.1: “Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.”

Common Core State Standards HSF.TF.A.2: “Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.”

Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.