Trigonometric Problem-Solving Techniques

This section focuses on applying trigonometric functions to solve various geometric problems. It demonstrates how to use sine, cosine, tangent, and cotangent in practical scenarios.

Vocabulary: The Pythagorean theorem (a² + b² = c²) is often used alongside trigonometric functions in right triangle calculations.

Key concepts covered:

1. Using sine and cosine to find missing sides in right triangles
2. Applying tangent and cotangent to calculate angles
3. Solving problems involving equilateral and isosceles triangles

Example: In a problem where sin α = 0.8 and the hypotenuse is 50, the opposite side can be calculated as 50 * 0.8 = 40.

The page also introduces more complex scenarios, such as using trigonometric functions in non-right triangles and combining multiple trigonometric ratios to solve multi-step problems.

Highlight: Understanding how to select the appropriate trigonometric function based on the given information is crucial for efficient problem-solving.

Trigonometric Functions and Values

This page introduces fundamental trigonometric functions and their values for key angles. It covers sine, cosine, tangent, and cotangent for 30°, 45°, and 60°.

Definition: Trigonometric functions relate angles of a right triangle to ratios of its sides.

Key trigonometric values presented include:

• Sin 30° = 1/2
• Cos 30° = √3/2
• Tan 30° = 1/√3
• Cot 30° = √3
• Sin 45° = Cos 45° = 1/√2
• Tan 45° = Cot 45° = 1
• Sin 60° = √3/2
• Cos 60° = 1/2
• Tan 60° = √3
• Cot 60° = 1/√3

Highlight: Memorizing these values is crucial for solving trigonometric problems efficiently.

The page also demonstrates practical applications through several example problems, showing how to use these values to find unknown sides or angles in right triangles.

Example: In a right triangle with hypotenuse 10 cm and an angle of 60°, the opposite side can be calculated as 10 * sin 60° = 10 * (√3/2) ≈ 8.66 cm.