Reduction Formulas and Function Signs

This page delves deeper into trigonometric formulas, focusing on reduction formulas and the signs of trigonometric functions across all four quadrants. It provides a comprehensive overview of how to simplify trigonometric expressions involving angles greater than 90°.

The reduction formulas are presented in a clear, tabular format, showing how to express trigonometric functions of angles in terms of functions of acute angles. This is particularly useful for solving problems involving angles in different quadrants.

Vocabulary: Reduction formulas are trigonometric identities that allow us to express the trigonometric functions of any angle in terms of the functions of an acute angle (0° to 90°).

Example: sin(180° - θ) = sin θ, cos(180° - θ) = -cos θ, tan(180° - θ) = -tan θ

The page also includes a detailed breakdown of the signs of sine, cosine, tangent, and cotangent in each quadrant, reinforcing the concepts introduced on the previous page.

Highlight: Understanding reduction formulas and function signs is crucial for solving complex trigonometric equations and proving trigonometric identities.

This information is essential for students studying advanced trigonometry and preparing for higher-level mathematics courses.

Radian Measure and Trigonometric Function Values

The final page introduces the concept of radian measure and provides a table of trigonometric function values for common angles. It explains how to convert between degrees and radians, which is crucial for many applications in physics and engineering.

Definition: A radian is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. One complete revolution is 2π radians.

The page presents formulas for converting between degrees and radians:

1. Degrees to radians: (π/180°) × angle in degrees
2. Radians to degrees: (180°/π) × angle in radians

Example: π/2 radians = 90°, π/4 radians = 45°

A comprehensive table of trigonometric function values for angles 0°, 30°, 45°, 60°, and 90° is provided, which is invaluable for quick reference and problem-solving.

Highlight: Memorizing these common angle values is essential for efficient problem-solving in trigonometry and related fields.

This page serves as a quick reference guide for students and professionals working with trigonometric calculations and angle measurements in various applications.