Year 10 - Maths
Calculate trigonometric ratios for 0°, 45° and 90°
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 calculate trigonometric ratios for 0°, 45° and 90°.
Key Notes
- The trigonometric ratios for 45° can be calculated using a square
- The square should have lengths of 1 unit
- By splitting the square into two right-angled triangles, you can calculate the ratio
- The ratios for 0° and 90° can be reasoned
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
- Trigonometry always involves rounding.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The trigonometric ratios for 45° can be calculated using a square. The square should have lengths of 1 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: Trigonometry always involves rounding. Correction: Try evaluating sin(0) on your calculator. What answer do you get?
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 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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