Final Chapters

Question 1

Rectangular to polar

Find theta

Answer 1

Tan^-1(y/X) if X>0

Tan^-1(y/X) + pie if X 0

3pie/2 if X=0 and y

Question 2

Polar to rectangular

Answer 2

X=rcos

Y=rsin

Question 3

R=2asin

R=-2asin

R=2acos

R=-2acos

Answer 3

Radius a for all

Center (0,a)

Center (0,-a)

Center (a,0)

Center (-a,0)

Question 4

Symmetric with X axis

Answer 4

Replace theta with - theta

If same equation then it is symmetric

Question 5

Symmetric with y axis

Answer 5

Replace theta with pie-theta

If same equation. Then is symmetric

Question 6

Symmetric with pole/origin

Answer 6

Replace r by -r

If same equation then is symmetric

Question 7

Cardioid with inner loop equations

Answer 7

R=a(1+cos)

R=a(1-cos)

R=a(1+sin)

R=a(1-sin)

Question 8

Limacons w/inner loop

Answer 8

R=a+bcos

R=a-bcos

R=a+Bsin

R=a-Bsin

Where a>0 . b>0 . a>b

Question 9

Limacons with inner loop

Answer 9

R=a+bcos

R=a-bcos

R=a+bsin

R=a-bsin

A>0. B>0. A

Question 10

Rose

Answer 10

R=acos(N theta)

R=asin(N theta)

If n is even then double amount of petal is n

If n is odd then n number of petals.

Question 11

a+bi

Answer 11

a-bi(a+bi)

Question 12

i^2

Answer 12

-1

Question 13

Norm of Z

Answer 13

Square root of (z)(complex conjugation of z)

Question 14

X+iy

Answer 14

Rcos+irsin

Question 15

Z1(Z2)

Answer 15

r1r2(cos(theta1+theta2) + isin(theta1+theta2))

Question 16

Z1/Z2

Answer 16

r1/r2(cos(theta1-theta2) +isin(theta1-theta2))

Question 17

Vector from one to another

Answer 17

Head -tail

P1 tail

P2 head

Question 18

Adding vectors

V+w

Answer 18

<a> </a>

Question 19

Subtracting vectors

V-W

Answer 19

V+ (-1)W

Question 20

Magnitude

||V||

Answer 20

Square root of a squared +b squared

Question 21

Dot product

V•W

Answer 21

ac+bd

Question 22

Finding theta

Answer 22

Cos(theta) = V•W / (||V||•||W||)

Question 23

Magnitude

Answer 23

||V||^2=a^2+b^2=V•V

Question 24

Parellel

Answer 24

Lie on same line
If
V=aW for some a number

Question 25

Orthangonal

Answer 25

Right angle

If V•W=0

Question 26

Projection of V1

Answer 26

V1=V•W / W•W (W)

Question 27

Projection V2

Answer 27

V-V1

Question 28

Work

Answer 28

F•PQ

Question 29

Rectangular to polar

To find r

Answer 29

Square root X squared plus y squared