MA30-02 Maths Coming soon
Trigonometric ratios: labelling sides and choosing sin, cos or tan
This lesson is coming soon.
In this lesson
Label the hypotenuse, opposite and adjacent sides of a right-angled triangle relative to a marked angle, choose the correct ratio (sin, cos or tan) for the information given, and recall the exact sin/cos values for 0, 30, 45, 60, 90 degrees and tan for 0, 30, 45, 60 degrees.
What it covers
- Identify the hypotenuse (always opposite the right angle, in any orientation of triangle)
- Label opposite and adjacent relative to a specific marked angle, and see that opposite and adjacent swap if a different angle in the same triangle is marked instead
- Use SOHCAHTOA to decide which ratio (sin, cos or tan) connects the labelled sides and the angle you have
- Recall the exact values of sin/cos at 0, 30, 45, 60, 90 degrees and tan at 0, 30, 45, 60 degrees, including deriving them from an equilateral triangle (30/60) and a right-angled isosceles triangle (45) as a memory aid rather than a bare table
Key words
For: Cambridge IGCSE 0580, Edexcel IGCSE 4MA1, AQA GCSE 8300, Edexcel GCSE 1MA1, Eduqas GCSE C300, OCR GCSE J560
On the specification
| Board | Spec | Statement |
|---|---|---|
| Cambridge IGCSE 0580 | C6.2 | Know and use the sine, cosine and tangent ratios for acute angles in calculations involving sides and angles of a right-angled triangle. |
| Cambridge IGCSE 0580 | E6.2 | Know and use the sine, cosine and tangent ratios for acute angles in calculations involving sides and angles of a right-angled triangle. |
| Cambridge IGCSE 0580 | C6.3 | Extended content only. |
| Cambridge IGCSE 0580 | E6.3 | Exact trigonometric values |
| Edexcel IGCSE 4MA1 | F4.8B | Know, understand and use sine, cosine and tangent of acute angles to determine lengths and angles of a right-angled triangle |
| Edexcel IGCSE 4MA1 | F4.8C | Apply trigonometrical methods to solve problems in two dimensions |
| AQA GCSE 8300 | G20 | Know the formulae for: Pythagoras’ theorem, a² + b² = c² and the trigonometric ratios, sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse and tanθ = opposite/adjacent |
| AQA GCSE 8300 | G21 | Know the exact values of sinθ and cosθ for θ = 0°, 30°, 45°, 60° and 90° |
| Edexcel GCSE 1MA1 | G20 | Know the formulae for: Pythagoras’ theorem a² + b² = c², and the trigonometric ratios, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent; apply them to find angles and lengths in right-angled triangles in two-dimensional figures |
| Edexcel GCSE 1MA1 | G21 | Know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60° |
| Eduqas GCSE C300 | FG18 | Know the formulae for: Pythagoras' theorem, a² + b² = c², and the trigonometric ratios, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent; apply them to find angles and lengths in right-angled triangles in two dimensional figures |
| Eduqas GCSE C300 | FG19 | Know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60° |
| Eduqas GCSE C300 | HG21 | Know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60° |
| OCR GCSE J560 | 10.05b | Know and apply the trigonometric ratios, sin θ, cos θ and tan θ and apply them to find angles and lengths in right-angled triangles in 2D figures. |
| OCR GCSE J560 | 10.05c | Know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°. Know the exact value of tan θ for θ = 0°, 30°, 45° and 60°. |
For teachers
This GCSE Maths lesson teaches trigonometric ratios: labelling sides and choosing sin, cos or tan. By the end, students should be able to label the hypotenuse, opposite and adjacent sides of a right-angled triangle relative to a marked angle, choose the correct ratio (sin, cos or tan) for the information given, and recall the exact sin/cos values for 0, 30, 45, 60, 90 degrees and tan for 0, 30, 45, 60 degrees. It works through two worked examples and the mistakes examiners report.