Year 9 - Maths
Using the tangent ratio
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 use the tangent ratio to find the missing side or angle in a right-angled triangle.
Key Notes
- The tangent ratio involves the opposite, adjacent and the angle.
- If you know the length of the opposite and the size of the angle, you can use the tangent ratio.
- If you know the length of the adjacent and the size of the angle, you can use the tangent ratio.
- If you know the length of the opposite and adjacent, you can use the tangent ratio.
Vocabulary To Learn
- Trigonometric functions: Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle containing the angle.
- Tangent function: The tangent of an angle (tan(θ°)) is the y-coordinate of point Q of the triangle which extends from the unit circle.
- Adjacent: The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle.
- Opposite: The opposite side of a right-angled triangle is the side which is opposite the marked angle.
Common Mistakes To Avoid
- Pupils may get the fraction (opposite/adjacent) inverted and this will still return an answer so they may believe they are correct.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The tangent ratio involves the opposite, adjacent and the angle. If you know the length of the opposite and the size of the angle, you can use the tangent ratio.
2. Use this key word in a maths sentence and explain it clearly. 'Trigonometric functions'
Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle containing the angle. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may get the fraction (opposite/adjacent) inverted and this will still return an answer so they may believe they are correct. Correction: Remind pupils to sense check their answers. The larger the angle, the longer the opposite side will be.
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
- Scaling the right-angled triangle from the unit circle 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
Browse all guides in the Year 9 Maths guide library.