pre calc unit 3 b Polar

polar coordinates

every point can be represented either with rectangular coordinates (x,y) or polar coordinates (r,θ)

polar to rectangular (y-axis)

y=r(sinθ)

polar to rectangular (x-axis)

x=r(cosθ)

Rectangular to polar

tanθ=y/x

rectangular to polar

r²=x²+y²

polar function r=f(θ) consists of ordered pairs (r,θ)

where input values are angle measures θ and out put values are radi r

polar graph circle (x-axis)

polar graph circle (y-axis)

what is “a” in a circle graph equation

polar graph rose (y-axis)

polar graph rose (x-axis)

what is the difference when n is even vs when n is odd? (rose polar graph)

polar graph limacon (x-axis)

polar graph limacon (y-axis)

what happens when a<b (limacon polar graph)

what happens when a>b (limacon polar graph)

what happens when a=b (limacon polar graph)

polar graph lemniscate (x-axis)

polar graph lemniscate (y-axis)

Multiplying complex #'s in polar form

Dividing complex #'s in polar form

Demoivre'S theorem

Roots of complex # ‘s( nth root)

Roots of complex # equation

Complex plane

Absolute value of a complex plane

Used to find distance between origin & point (A, B)

Trigonometric/polar equation