Year 10 - Maths
Applying trigonometric ratios in context
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 apply trigonometric ratios to practical situations including angles of elevation and depression.
Key Notes
- Trigonometric ratios are used in many scenarios
- Trigonometric ratios are used to calculate the height of a structure
Vocabulary To Learn
- Trigonometric functions: 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.
- Cosine function: The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.
- 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
- Using the wrong trigonometric function.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Trigonometric ratios are used in many scenarios. Trigonometric ratios are used to calculate the height of a structure.
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 for a given angle. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Using the wrong trigonometric function. Correction: Encourage pupils to draw the right-angled triangle for the scenario if they are unsure so that they can label the sides and be confident about which trigonometric function is needed.
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
- 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 cosine problems 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
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