Study Fact Sheet 6 - Jake Venditto Groom Sinusoidal...

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Jake Venditto 12/14/09 Groom Study Fact Sheet Sinusoidal Functions and Polar Coordinates Sine and Cosine Curves Y = A sin(B(θ-h)) + K A = Amplitude B = Frequency 2π/B =Period h = horizontal shift y = k : Midline, Vertical shift Ex. Y = 2 sin(2θ-π) + 1 Plot Polar Coordinates on Polar Paper Given the point A: (4, π) Convert π into degrees (180°) Travel around from 0 to 180 Then move out from the origin 4 units Given the Point B: (-2, 5π 6) Convert radians into degrees: 150° Travel around from 0 to 150 Then move in the opposite direction 2 units A B
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Converting Rectangle Coordinates Into Polar: r = x² + y² θ = Tan (y/x) Example: (r, θ) = (-1,1) r = x² + y² Tan (-1/1) = -45° 135° 135° = 3π/4 r = ( 2 , ) Converting Polar to Rectangular ( r cos(θ) , r sin(θ) ) Example: (2, π) = (x, y) x = 2 cos π y = 2 sin π x = 2 (-1) y = 2 (0) (-2, 0) x = -2 y = 0 Polar Curves Circles: Ex. r = 3Cos(θ) r = 3Sin(θ) The given diameter of the circle is the number multiplied by sin(θ) or cos(θ)
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Study Fact Sheet 6 - Jake Venditto Groom Sinusoidal...

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