Page 2: Cosine Function Analysis

The cosine function $y = cos x$ shares many similarities with sine but with a phase shift. This section explores the distinctive features of the cosine graph.

Definition: The cosine function is a periodic function with the same period as sine but shifted 90° to the left.

Key characteristics of the cosine function include:

• X-axis crossings at 90°, 270°, and their multiples
• Maximum value of 1 occurs at 0° and 360°
• Minimum value of -1 occurs at 180°

Highlight: The cosine function starts at its maximum value (1) at 0°, unlike sine which starts at 0.

Page 3: Tangent Function Analysis

This page explores Understanding tanx asymptotes and crossing points and their significance in trigonometric analysis.

Vocabulary: Asymptotes are straight lines that a curve approaches but never actually meets.

The tangent function displays unique characteristics:

• X-axis crossings at 0°, 180°, 360°
• Asymptotes occur at 90°, 270°, and their multiples
• Range extends from negative infinity to positive infinity

Highlight: Unlike sine and cosine, the tangent function has no amplitude restrictions and includes vertical asymptotes.

Example: The tangent value at 45° is 1, while at 90° it approaches infinity, demonstrating the function's unbounded nature.

Page 1: Sine Function Analysis

The sine function $y = sin x$ demonstrates fundamental periodic behavior across a 360-degree cycle. This page details the comprehensive analysis of Prigonometry sin and cos graph features.

Definition: The sine function is a periodic function that repeats every 360 degrees or 2π radians.

Highlight: Key features of the sine graph include regular x-axis crossings and consistent maximum and minimum values.

The sine function exhibits several crucial characteristics:

• X-axis crossings occur at 0°, 180°, 360° and their multiples
• Maximum turning points occur at 90° with a value of 1
• Minimum turning points occur at 270° with a value of -1

Example: At 30°, sin x = 0.5, demonstrating the gradual increase from 0° to the maximum at 90°.