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Grade 10 Math Lab: Proof & Generalization FREE

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Cosine Function & Graphing

60 min Grade 10 Math Lab: Proof & Generalization

Learning Objectives

Graph y = A·cos(Bx + C) + D
Identify amplitude, period, phase shift
Model periodic phenomena

Key Concepts

Amplitude

|A| — maximum displacement from midline

Period

2π/|B| — length of one complete cycle

Theory

**y = A·cos(Bx + C) + D** - A: Amplitude (vertical stretch) - B: Affects period (2π/B) - C/B: Phase shift (horizontal shift) - D: Vertical shift (midline) **cos vs sin:** cos(x) = sin(x + π/2) — cosine leads sine by 90°.

Examples

Find period of y = 3cos(2x)

Solution: Period = 2π/2 = π