AP Pre Calc 3.13-3.15 QUIZ

Polar radius

x²+y²=r²

Polar angle

Arctan/tan^-1 (y/x)

convert polar to rectangular for the x-coordinate

x=rcos(theta)

convert polar to rectangular for the y-coordinate

y=rsin(theta)

loop graph

r=a*sin(n*theta)

what does a and b do in a loop graph

a changes the size of the loops; b changes the amount of loops

rose graphs

r=acosbtheta

what does a and b do in a rose graph

a changes the size of the petals; b changes the amount of petals (even numbers double petals; odd stays the same)

Limacon graphs

r=a+bsintheta; r=a+bcostheta

what does a and b do in a limacon graph

a makes the outer circle expand; b makes the whole thing expand

what does cos and sin do in a limacon graph

sin keeps the graph upright; cos rotates the graph on its side

Cardioid graphs

r=a+bcostheta

what does a and b do in a cardioid graph

a makes the graph bigger; b adds a second loop at the bottom

spiral of archimedes graph

r=theta

Lemniscate graph

r²=a²cos2theta / r²=a²sin2theta

what does a do in a lemniscate graph

it makes the graph bigger/smaller

what does cos and sin do in a lemniscate graph

cos is the graph horizontal; sin is rotated on a diagonal