Year 9 - Maths
Sine and cosine ratios
Trigonometry
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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 sine and cosine ratios from the sides of a right-angled triangle.
Key Notes
- When the hypotenuse has a length of one, the opposite side has length sin(θ)
- When the hypotenuse has a length of one, the adjacent side has length cos(θ)
- Any right-angled triangle is a scaled version of this triangle.
Vocabulary To Learn
- Hypotenuse: The hypotenuse is the side of a right-angled triangle which is opposite the right 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.
- 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.
Common Mistakes To Avoid
- sin(60°) is double sin(30°).
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
When the hypotenuse has a length of one, the opposite side has length sin(θ). When the hypotenuse has a length of one, the adjacent side has length cos(θ).
2. Use this key word in a maths sentence and explain it clearly. 'Hypotenuse'
The hypotenuse is the side of a right-angled triangle which is opposite the right angle. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: sin(60°) is double sin(30°). Correction: The values of the sine or cosine of an angle do not scale linearly. We can see from the unit circle that an angle of 30° meets the circle at a height of 0.5 units, whilst an angle of 60° meets the circle at a height of approximately 0.87 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
- 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.