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- Year 10•
- Higher
Checking and securing understanding of the unit circle
I can see how the trigonometric functions are derived from measurements within a unit circle and how this can be utilised.
- Year 10•
- Higher
Checking and securing understanding of the unit circle
I can see how the trigonometric functions are derived from measurements within a unit circle and how this can be utilised.
Lesson details
Key learning points
- Trigonometric functions are derived from measurements within a unit circle
- The right-angled triangle within the unit circle has a hypotenuse of length one unit
- The triangle can be scaled to any other right-angled triangle
- Similar triangles have the same interior angles
- Similar triangles have the same trigonometric ratios
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.
Common misconception
When reading the values of the trigonometric functions during the explanation slides and the tasks, pupils may think that all the values taken from the graphs are fully accurate.
Explain that many of the values from the trigonometric functions have digits beyond the second decimal place. Their calculator has these values stored to far more decimal places.
To help you plan your year 10 maths lesson on: Checking and securing understanding of the unit circle, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Checking and securing understanding of the unit circle, 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 Right-angled trigonometry unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.A tangent to a curve at a given point is a line that intersects the curve at that point. Both the tangent and the curve have the same at the given point.
Q2.What are the coordinates of P?
Q3.What are the coordinates of Q?
Q4.A right-angled triangle has a hypotenuse of 1 cm and a short side of 0.6 cm, what is the length of the third side of the triangle?
Q5.A right-angled triangle has a hypotenuse of 1 cm and a short side of 0.54 cm, what is the length of the third side of the triangle, to 2 decimal places?
Q6.A right-angled triangle has a hypotenuse of 2.6 cm and a short side of 1 cm, what is the length of the third side of the triangle?
Assessment exit quiz
6 Questions
Q1.What are the features of the unit circle?
Q2.The sine of an angle is the __________ of the point where the radius of the unit circle has been rotated through that angle.
Q3.The __________ of an angle is the $$x$$-coordinate of the point where the radius of the unit circle has been rotated through that angle.
Q4.The tangent of an angle is the __________ of the point where the line (the triangle’s hypotenuse) intersects the tangent line.
Q5.Match up the correct trigonometric values.
$$\sin(50^\circ)$$ -
0.77
$$\cos(50^\circ)$$ -
0.64
$$\tan(50^\circ)$$ -
1.19
Q6.Using this diagram, what can be deduced?
