Trigonometric Functions

This lesson covers the graphs, properties and transformations of the sine, cosine and tangent functions. Understanding these graphs is essential for solving equations and modelling periodic phenomena at A-Level (9MA0).

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The Sine Function: y = sin(x)

Key Properties

Property	Value
Period	2pi (360 degrees)
Amplitude	1
Range	-1 <= y <= 1
Symmetry	Odd function: sin(-x) = -sin(x)
Key points	sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1
Zeros	x = n x pi, where n is any integer

The sine curve starts at the origin, rises to 1 at pi/2, returns to 0 at pi, drops to -1 at 3pi/2, and returns to 0 at 2pi.

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The Cosine Function: y = cos(x)

Key Properties