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