Study Notes
Right-angled trigonometry involves understanding triangles with one angle of 90 degrees, applying the Pythagorean theorem, and using trigonometric ratios to solve problems.
- Right-angled triangle — a triangle with one angle equal to 90 degrees. Example: In triangle ABC, angle C is 90 degrees.
- Hypotenuse — the longest side of a right-angled triangle, opposite the right angle. Example: In triangle ABC, if angle C is 90 degrees, then side AB is the hypotenuse.
- Pythagorean theorem — states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Example: In triangle ABC, if AB is the hypotenuse, then AB² = AC² + BC².
- Sine (sin) — a trigonometric ratio defined as the opposite side over the hypotenuse. Example: sin(θ) = opposite/hypotenuse.
- Cosine (cos) — a trigonometric ratio defined as the adjacent side over the hypotenuse. Example: cos(θ) = adjacent/hypotenuse.
- Tangent (tan) — a trigonometric ratio defined as the opposite side over the adjacent side. Example: tan(θ) = opposite/adjacent.
Exam Tips
Key Definitions to Remember
- A right-angled triangle has one angle of 90 degrees.
- The hypotenuse is the longest side of a right-angled triangle.
- Pythagorean theorem: c² = a² + b².
- Sine, cosine, and tangent are trigonometric ratios.
Common Confusions
- Confusing the hypotenuse with other sides.
- Mixing up sine, cosine, and tangent ratios.
Typical Exam Questions
- What is the length of the hypotenuse if the other sides are 3 cm and 4 cm? Answer: 5 cm
- How do you calculate the sine of an angle in a right-angled triangle? Answer: Opposite side divided by hypotenuse
- What is the cosine of a 45-degree angle in a right-angled triangle? Answer: 1/√2 or approximately 0.707
What Examiners Usually Test
- Ability to identify and label sides of a right-angled triangle.
- Application of the Pythagorean theorem to find missing sides.
- Use of trigonometric ratios to calculate angles and sides.