final

Question 1

Component form of a vector

Answer 1

{a,b}, {Δx, Δy}
{|v|cos θ, |v|sin θ}

Question 2

Magnitude

Answer 2

the length of the vector, in word problems distance or force
|v|= √a^2 + b^2

Question 3

Directional angle

Answer 3

Always positive, referenced from the -positive x-axis
tan^-1b/a

Question 4

Polars

Answer 4

Points have coordinates (r,θ),
- | r | is the radius
- | θ | is the counterclockwise angle
- If r is negative, the point is reflected over the pole (origin)
- If θ is negative, it is the clockwise angle

Question 5

Complex Plane

Answer 5

Graphing numbers in the form of a + bi
Horizontal axis: a
Vertical axis: b
Points become (a, b)

Question 6

Complex number to polar form

Answer 6

(a, b) = (rcosθ, rsinθ), making Z = a + bi = r(cosθ + isinθ) or r(cisθ)

where r = radius (it’s also factored out of the sum)

Question 7

Pythagorean identities

Answer 7

sin^2x+cos^2x=1
tan^2x+1=sec^2x
1+cot^2=csc^2

Question 8

tan and cot identities

Answer 8

tanx = sinx/cosx
cotx = cosx/sinx

Question 9

double angle identities

Answer 9

sin2x = 2sinxcosx
cos2x = cos^2x-sin^2x OR 1-2sin^2 OR 2cos^2x-1
tan2x = 2+tanx/1-tan^2x

Question 10

sum and difference identities

Answer 10

sin(x+y) = sinxcosx + cosxsiny
sin(x-y) = sinxcosx - cosxsiny
cos(x+y) = coxcosy - sinxsiny
cos(x-y) = cosxcosy + sinxsiny
tan(x+y) = tanx +tany/1-tanxtany
tan(x-y) = tanx-tany/1+tany

Question 11

resultant vectors

Answer 11

{x1 + y1, x2 + y2}
Also works for subtraction

Question 12

complex properties

Answer 12

z1z2 = r1r2(cisθ+θ)
z1/z2= r1/r2(cisθ-θ)

Question 13

complex powers

Answer 13

z^n=r^n((cosnθ+isinθ)

Question 14

complex roots

Answer 14

n√r(cosθ+2pik/n + isinθ+2pik/n)
must solve for all values of n and k
n = root, k=n-1

Question 15

law of sines

Answer 15

a/sinA = b/sinB = c/sinC

Question 16

law of cosines

Answer 16

a^2 = b^2 + c^2 - bc(cosA)

Question 17

Area with sines

Answer 17

1/2ab*sinc

Question 18

Heron’s formula

Answer 18

s = a+b+c/2
√s(s-a)(s-b)(s-c)