Year 10 - Maths
Checking and securing understanding of the unit circle
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 see how the trigonometric functions are derived from measurements within a unit circle and how this can be utilised.
Key Notes
- Trigonometric functions are derived from measurements within a unit circle
- The right-angled triangle within the unit circle has a hypotenuse of length one unit
- The triangle can be scaled to any other right-angled triangle
- Similar triangles have the same interior angles
- Similar triangles have the same trigonometric ratios
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
- When reading the values of the trigonometric functions during the explanation slides and the tasks, pupils may think that all the values taken from the graphs are fully accurate.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Trigonometric functions are derived from measurements within a unit circle. The right-angled triangle within the unit circle has a hypotenuse of length one unit.
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: When reading the values of the trigonometric functions during the explanation slides and the tasks, pupils may think that all the values taken from the graphs are fully accurate. Correction: Explain that many of the values from the trigonometric functions have digits beyond the second decimal place. Their calculator has these values stored to far more decimal places.
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 cosine problems Study Guide
- Checking and securing understanding of sine ratio problems Study Guide
- Checking and securing understanding of tangent ratio problems 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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