2_PolarII - Polar Graphing Graph inequalities ex 2 3 2 r ex 0 r 1 ex r = 3 Circle with radius 3 and center at origin The equation for a circle with

2_PolarII - Polar Graphing Graph inequalities ex 2 3 2 r ex...

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Polar Graphing Graph inequalities ex. θ = 2 π 3 , - 2 r ex. 0 < θ π , r = 1
ex. r = 3 Circle with radius 3 and center at origin. The equation for a circle with radius a and center at the origin is r = a . ex. θ = π 3 The equation of a line through the origin is θ = # .
Recall x 2 + y 2 = r 2 x = r cos θ y = r sin θ tan θ = y x Polar to Cartesian ex. r = 3 ex. θ = π 3 ex. r = - 6 cos θ
ex. r = 2cos θ
Cartesian to Polar ex. y = x ex. x 2 - y 2 = 1
Polar to Parametric ex. r = 3 ex. r = - 6 cos θ
Do: 1. Find the Cartesian equation for 2 r 2 co s θ s in θ = 1 . 2. Find the polar equation for x 2 + y - 4 (29 2 = 16 . (Hint: Multiply it out first.) 3. Find parametric equations for r = θ .
More graphing. ex. r = sin θ Find values of sine for θ = 0, π 2 , π , 3 π 2 ,2 π . Plot these points on the graph. Plot the graph for r > 0 and then again for r < 0.
ex. r = sin4 θ For sin( n θ ) , find values for θ = 0, π 2 n , 2 π 2 n , 3 π 2 n , 4 π 2 n ,etc. . In this example we will find values for θ = 0, π 8 , π 4 , 3 π 8 , π 2 etc. Plot these on the graph.
ex. r = 1 - 2sin2 θ Find values for find values for θ = 0, π 4 , π 2 , 3 π 4 , π , 5 π 4 , 3 π 2 , 7 π 4 ,2 π Plot these points.

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