Year 9 - Maths
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 derive the tangent ratio from the sides of a right-angled triangle.
Key Notes
- When the adjacent has a length of one, the opposite side has a length of tan(θ).
- You can apply a scale factor to this triangle to find the scaled length of the opposite side.
- There is a multiplicative link between two similar right-angled triangles.
- There is a multiplicative link within each right-angled triangle.
Vocabulary To Learn
- 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.
- Trigonometric ratios: The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.
- 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 Mistakes To Avoid
- tan(60°) is double tan(30°).
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
When the adjacent has a length of one, the opposite side has a length of tan(θ). You can apply a scale factor to this triangle to find the scaled length of the opposite side.
2. Use this key word in a maths sentence and explain it clearly. 'Adjacent'
The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: tan(60°) is double tan(30°). Correction: The values of tan of an angle do not scale linearly. From the unit circle, we see that an angle of 30° meets a tangent to the circle at a height of approx. 0.58 units, whilst an angle of 60° meets the same tangent at a height of approx. 1.73 units.
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
- 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.