Interpreting the trigonometric graphs
I can read values from the graphs and can identify how many solutions exist within a given range.
Interpreting the trigonometric graphs
I can read values from the graphs and can identify how many solutions exist within a given range.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- Reading solutions from trigonometric graphs is the same as reading solutions from any other graph
- Due to the period, there may be more than one solution
- It is possible to predict the number of solutions that exist within a given range
Keywords
Trigonometric functions - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.
Sine function - The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.
Cosine function - The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.
Tangent function - The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.
Period (of a function) - For a repeating function, the period is the distance of one repetition of the entire function.
Common misconception
Pupils assume that the graph displayed always shows the number of solutions.
It is important to compare the range of values that the graph is displaying against what is being defined in the question.
To help you plan your year 11 maths lesson on: Interpreting the trigonometric graphs, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Interpreting the trigonometric graphs, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Non right-angled trigonometry unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Starter quiz
6 Questions
$$\tan(20°)$$ -
0.364 (3 s.f)
$$\tan(80°)$$ -
5.67 (3 s.f)
$$\tan(97°)$$ -
-8.14 (3 s.f)
$$\tan(105°)$$ -
-3.73 (3 s.f)
$$x = 5$$ -
$$y = 25$$
$$x = 2$$ -
$$y = 4$$
$$x = -3$$ -
$$y = 9$$
$$x = 8$$ -
$$y = 64$$
$$x = -6$$ -
$$y = 36$$