Pre-Cal Chapter 9
(9.1) Polar Coordinates representations
(r,θ + 2πk) or (-r,θ + 2πk) k any integer
(9.3) Complex Plane
A plane that represents all complex numbers in the z = x + yi (x,y)
(9.1) Pole
A point in a polar graph that is the initial point of in graph from which distance is measured
(9.1) Polar axis
A ray with a vertex that is a pole from which angles are measured
(9.1) Polar coordinates
An ordered pair (r,θ) that uniquely determines a point on a polar graph
(9.3) Absolute Value of z
Another name fpr Magnitude or Modulus
(9.2) Graph Polar Equations
Determine if symmetries exist and find r values using θ values producing exact
(9.1) Two of Four Steps for Rectangular to Polar
Determine r from conversion formula
(9.1) One of Four Steps for Rectangular to Polar
Determine the Quadrant from the sign of x & y
(9.1) Four of Four Steps for Rectangular to Polar
Determine θ from quadrant and reference angle from formula
(9.2) Symmetry with respect to the Pole
Equaivalent equation when r is replaced with -r
(9.2) Polar Equation
Equations with polar coordinate variables
(9.1) Three of Four Steps for Rectangular to Polar
If x and/or y is 0 determine the position on x or y axis
(9.2) Graph of polar Equation
Points on a graph consisting of Polar coordinates that satisfy a polar equation
(9.3) Definition Magnitude (Modulus)
The distance from the origin
(9.3) Real Axis
The x axis representing the real numbers
(9.3) Imaginary Axis
The y axis representing the imaginary numbers
(9.2) Symmetry with respect to Polar Axis
f(-θ)=f(θ)
(9.2) Symmetry with respect to θ = π/2
f(π - θ)=f(θ)
(9.2) Horizontal ine in Polar terms
r Cos θ = a (a nonzero)
(9.2) Vertical line in polar terms
r Sin θ = a (a nonzero)
(9.2) Circle in polar terms
r= 2a Sin θ or 2a Cos θ
(9.1) Conversion polar to Rectangular formulas
x=rcos θ y = rSin θ
(9.3) Polar form of a complex number
z = r(Cos θ + iSin θ)
(9.3) Rectangular form of a complex number
z = x + yi