Chapter 6

Question 1

Law of Sines

Answer 1

SinA/a = SinB/b = SinC/c

Question 2

Law of Cosines

Answer 2

a² = b² + c² - 2bcCosA

Question 3

ALT Law of Cosines

Answer 3

CosA = b² + c² - a² / 2bc

Question 4

When drawing out a triangle

Answer 4

Think about it phsyically

Question 5

Inner angles add up to

Answer 5

180°

Question 6

Component Form

Answer 6

Terminal Minus Initial (TMI)
⟨x₂-x₁, y₂ - y₁⟩

Question 7

Linear Combination Form

Answer 7

xi +- yj

Question 8

Magnitude

Answer 8

√x² + y²

Question 9

Unit Vector

Answer 9

⟨x/||x||, y/||y||⟩
or ⟨x/mag, y/mag⟩

Question 10

Vector Operations

Answer 10

u + v = ⟨u_x + v_x, u_y + v_y⟩

#u = ⟨#u_x, #u_y⟩

-v = ⟨-v_x, -v_y⟩

u - v = ⟨u_x - v_x, u_y - v_y⟩

Question 11

Dot Product

Answer 11

u·v = u_x · v_x + u_y · v_y

Question 12

Angle Between

Answer 12

cosθ = u·v/(||u||)·(||v||)
or
cosθ = u·v/(u magn)·(v magn)

Question 13

If angle between (cosθ) = 0

Answer 13

θ = 90°
vectors u and v are orthogonal (perpendicular)

Question 14

Bearing D₁ #° D₁

Answer 14

° From direction 1 to direction 2

Question 15

Area

Answer 15

1/2abSinC