Introduction to Trigonometry

The second page explores trigonometric ratios and their application in right-angled triangles. It focuses on the three main trigonometric functions: sine, cosine, and tangent.

Vocabulary: Key terms introduced include:

• Opposite: The side opposite to the angle in question
• Adjacent: The side next to the angle in question
• Hypotenuse: The longest side of the right triangle

Example: The page demonstrates calculating angles using inverse trigonometric functions:

• sin⁻¹(3) = 36.9°
• tan⁻¹(2) = 63.4°

Highlight: The relationship between sides and angles is clearly illustrated through trigonometric ratios, showing how to find unknown angles when side lengths are known.

Understanding Pythagorean Theorem

The first page introduces the fundamental concept of the Pythagorean theorem and its practical application in right-angled triangles. The theorem is expressed through the equation a² + b² = c², where c represents the hypotenuse and a and b represent the other two sides of the right triangle.

Definition: The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (longest side) equals the sum of squares of the other two sides.

Example: A right triangle with sides 2 and 4 has its hypotenuse calculated as follows: 2² + 4² = c² 4 + 16 = c² c = √20 ≈ 4.47

Highlight: Multiple worked examples demonstrate how to find missing sides using the theorem, including cases where the hypotenuse is known and one side needs to be calculated.