Year 9 - Maths
Scaling the right-angled triangle from the unit circle
Trigonometry
Study Hub
Study Guides
This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils learn how to recognise the relationship between the unit circle and the trigonometric ratios of sine, cosine and tangent. Pupils then apply this knowledge to solve trigonometric problems.
Lesson Summary
You will learn to recognise the right-angled triangle within a unit circle and use proportion to scale to similar triangles.
Key Notes
- There are specific ratios within the two key right-angled triangles defined by the unit circle.
- The first right-angled triangle has hypotenuse of length one.
- The opposite and adjacent sides of this triangle have lengths sin(θ) and cos(θ), respectively.
- The second right-angled triangle has an adjacent side length of one.
- The opposite side of this triangle has length tan(θ)
Vocabulary To Learn
- Trigonometric ratios: The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.
- Opposite: The opposite side of a right-angled triangle is the side which is opposite the marked angle.
- Adjacent: The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle.
Common Mistakes To Avoid
- 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.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
There are specific ratios within the two key right-angled triangles defined by the unit circle. The first right-angled triangle has hypotenuse of length one.
2. Use this key word in a maths sentence and explain it clearly. 'Trigonometric ratios'
The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: 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. Correction: Explain that many of the values from the trigonometric functions have digits beyond the second decimal place. However, two decimal places is a reasonable degree of accuracy for reading values from the graphs during this lesson.
More Lessons In This Unit
- Checking and securing understanding of Pythagoras' theorem Study Guide
- Checking and securing understanding of similar triangles Study Guide
- Choosing an appropriate method for finding lengths of a triangle Study Guide
- Choosing the right trigonometric ratio Study Guide
- Problem solving with trigonometry Study Guide
- Sine and cosine ratios Study Guide
- Tangent ratio Study Guide
- The unit circle Study Guide
- Using the cosine ratio Study Guide
- Using the sine ratio Study Guide
- Using the tangent ratio Study Guide
Browse all guides in the Year 9 Maths guide library.