math ch17: polar coordinate

used for example when air traffic controllers record the locations of airplanes using distances and angles

the location of the point P in the polar coordinate system can be identified by —— of the form —-

represents the directed distance from the pole to the point

represents the directed angle from the polar axis

if theta is positive, it indicates

if theta is negative, it indicates

r is positive, then p is on the

r is negative, then p lies on the

if the terminal side rotates one full circle, then it will

(r,theta)= two points similar to it if it rotates

if the terminal side rotates half circle. then it will land

(r,theta) as a half circle rotation will be

in both rotations, the value of r will —— but with half circle rotation it will be represented by —— to indicate that the point is on the ray——- to the terminal side of theta

an equation expressed in terms of polar coordinates is called

is the set of all points with coordinates (r,theta) that satisfy the given polar equation

if p1(r1,theta1) and p2(r1,theta2) are two points in the polar plane, then the distance between them is given by

in terms of r and theta x is

in terms of r and theta, y is

(x,y) in polar coordinates is called

r=(in terms of x and y)

if theta=tan^-1(y/x), then x is

f theta=tan^-1(y/x) + pi, then x is

the absolute value of the complex factor z= a + bi is IzI= I a+bi I=

the polar form of the complex number z= a + bi is z=

if theta= tan^-1 b/a, then a is

if theta= tan^-1 b/a + pi, then a is

if the polar form of a complex number is z=r(cos x + i sin x), then for the positive integers n:

z1z2=

if the polar form of a complex number is z=r(cos x + i sin x), then for the positive integers n:

z1/z2:

for a positive integer p, the complex number r(cos x + isinx) has distinct p roots. they are found by:

when n equals or exceeds p, then roots repeat as the following

argument=