eharetea

Tbe trigonometric sine function.

Sinusoidal waves.

Date Created:Saturday January 20th, 2007 09:06 AM
Date Modified:Saturday August 02nd, 2008 01:18 AM

SOHCAHTOA
sin = opposite/hypotnuese

ƒ(x) = sin(x)

ƒ(x)	x
0	0
π/2	1
π	0
3π/2	-1
2π	0

if evaluating on a circle of radius r, ƒ(θ) = sinθ = y/r



properties of: ƒ(x) = sin(x)

Period	2π sin(θ + 2π) = sinθ
Domain	All real numbers
Range	[-1,1]
Symmetry	over origin (odd function) sin(-θ) = -sinθ
Zeros	nπ; n is any integer ex: {π, 2π, 5π, etc...} (180°)

ƒ(x) = Asin(wx) + b

Period	2π/w
Amplitude	|A|
New x-axis	y=b

sinθ = cos(θ-π/2)
cosθ = sin(θ+π/2)

Quadrants

QII (-,+) + = positive	QI (+,+) + = positive
QIII (-,-) - = negative	QIV (+,-) - = negative