This document discusses converting between Cartesian and polar coordinates. It provides the definitions of sine, cosine, and tangent as ratios of opposite, adjacent, and hypotenuse in a right triangle. Examples are given of converting the point (4, 1500) to polar coordinates (2, -150 degrees) and deriving the equation r=3tanθ from the definition that x2 + y2 = r2.

1. Polar Coordinates!!Conversion from Cartesian to Polar Coordinates

2. Example Problems: ( 4, 150⁰) =>> (x , y) Soh Cah ToaSoh θ = Opp./Hyp.Cah θ = Adj./Hyp. Tan θ = Opp./Adj. x +y=rx150⁰4y222 sin 150 = x 4X = 4 sin 150X = 2Cos 150 = y 4Y = 4 cos 150Y = -3.46

3. 22x + y = 4 Soh Cah ToaSoh θ= Opp./Hyp.Cah θ= Adj./Hyp.Tan θ= Opp./Adj. x +y=r2r = 4r = 2222a circle is a constant radius around some point.

4. Soh Cah ToaSoh θ= Opp./Hyp. = y/rCah θ= Adj./Hyp. = x/rTan θ= Opp./Adj. = y/x x +y=r222( x + y ) = 9(y/x)r = 9( tanθ )r = 9 ( tan θ )r = 3 tan θ222222