Year 10 - Maths
Checking and securing understanding of cosine problems
Right-angled 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 are introduced to a variety of situations where trigonometric ratios are required, such as 3-D problems and problems of elevation or depression.
Lesson Summary
You will learn to use the cosine ratio to find the missing side or angle in a right-angled triangle.
Key Notes
- The cosine ratio involves the hypotenuse, adjacent and the angle
- If you know the length of the hypotenuse and the size of the angle, you can use the cosine ratio
- If you know the length of the adjacent and the size of the angle, you can use the cosine ratio
- If you know the length of the hypotenuse and adjacent, you can use the cosine ratio
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.
- Trigonometric functions: Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle containing the angle.
- Cosine function: The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.
Common Mistakes To Avoid
- The cosine formula is only used to find the length of a side adjacent to an angle.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The cosine ratio involves the hypotenuse, adjacent and the angle. If you know the length of the hypotenuse and the size of the angle, you can use the cosine 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 cosine formula is only used to find the length of a side adjacent to an angle. Correction: The cosine formula can be used to find the length of a side adjacent to an angle. A rearrangement of the formula also allows us to find the length of the hypotenuse given the adjacent side. The arccosine function allows us to find the angle, itself.
More Lessons In This Unit
- Advanced problem solving with right-angled trigonometry Study Guide
- Applying Pythagoras' theorem in 3D Study Guide
- Applying trigonometric ratios in 3D Study Guide
- Applying trigonometric ratios in context Study Guide
- Calculate trigonometric ratios for 0°, 45° and 90° Study Guide
- Calculate trigonometric ratios for 30° and 60° Study Guide
- Calculating the length of a line segment Study Guide
- Checking and further securing understanding of Pythagoras' theorem Study Guide
- Checking and securing understanding of sine ratio problems Study Guide
- Checking and securing understanding of tangent ratio problems Study Guide
- Checking and securing understanding of the unit circle Study Guide
- Problem solving with right-angled trigonometry Study Guide
- Using Pythagoras' theorem to justify a right-angled triangle Study Guide
Browse all guides in the Year 10 Maths guide library.