Year 9 - Maths
Using the sine ratio
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 use the sine ratio to find the missing side or angle in a right-angled triangle.
Key Notes
- The sine ratio involves the hypotenuse, opposite and the angle.
- If you know the length of the hypotenuse and the size of the angle, you can use the sine ratio.
- If you know the length of the opposite and the size of the angle, you can use the sine ratio.
- If you know the length of the hypotenuse and opposite, you can use the sine ratio.
Vocabulary To Learn
- Hypotenuse: The hypotenuse is the side of a right-angled triangle which is opposite the right angle.
- Opposite: The opposite side of a right-angled triangle is the side which is opposite the marked angle.
- Trigonometric function: 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.
Common Mistakes To Avoid
- The sine formula is only used to find the length of a side opposite an angle.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The sine ratio involves the hypotenuse, opposite and the angle. If you know the length of the hypotenuse and the size of the angle, you can use the sine ratio.
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: The sine formula is only used to find the length of a side opposite an angle. Correction: Whilst the sine formula can be used to find the length of a side opposite an angle, a rearrangement of the formula also allows us to find the length of the hypotenuse given the opposite side. The arcsine function allows us to find the angle, itself.
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 tangent ratio Study Guide
Browse all guides in the Year 9 Maths guide library.