Chapter 7-8 (Notecard to memorize)

Question 1

Law of Sine

Answer 1

1. (sin A) / a = (sin B) / b = (sin C) / c
2. a / (sin A) = b / (sin B) = c / (sin C)

Question 2

Area of triangle (SAS)

Answer 2

A = 1/2 ab sin C
A = 1/2 bc sin A
A = 1/2 ac sin B

Question 3

Law of Cosine

Answer 3

1) a^2 = b^2 + c^2 - 2 bc cos A
2) b^2 = a^2 + c^2 - 2 ac cos B
3) c^2 = a^2 + b^2 - 2 ab cos C

Question 4

Ambiguous Case for Law of Sine

Answer 4

Check second triangle

Question 5

Heron Formula for word problem

Answer 5

Step 1: S = 1/2(a + b + c)
Step 2: A = √(S(S - a)(S - b)(S - c))
Step 3: # bag = Area that found above Step 2 / ground cover (sq ft)

Question 6

Find the angle between two vectors

Answer 6

cos θ = (u1 v1) + (u2 v2) / √(u1^2 + u2^2) √(v1^2 + v2^2)

Question 7

i²

Answer 7

• 1

Question 8

i³

Answer 8

• i

Question 9

i⁴

Answer 9

1

Question 10

i

Answer 10

√-1

Question 11

Trig form

Answer 11

z = r (cosθ + i(sinθ)) = r cis θ

Question 12

Rectangular Form

Answer 12

z = x + y1

Question 13

z1z2

Answer 13

r1r2 cis (θ1 + θ2)

Question 14

z1÷z2

Answer 14

r1 ÷ r2 cis (θ1 - θ2)

Question 15

Demoivre’s Theorem

Answer 15

zn= rncis(n(θ))

Question 16

nth Root Theorem (Finding roots)

Answer 16

Degree: ak= n√r cis ((θ + 360∘k) ÷ n)

Question 17

Radian Mode (nth Root Theorem)

Answer 17

ak= n√r cis ((θ + 2kπ) ÷ n)

Question 18

Sine (Polar Graph Equation)

Answer 18

Start Quad 1 then Quad 3 for second time

Question 19

Reflection for Sine Polar graph

Answer 19

Q1 to Q2 and Q3 to Q4

Question 20

Cosine (Polar Graph Equation)

Answer 20

Start Quad 1 then Quad 2 for second time

Question 21

Reflection for Cosine Polar graph

Answer 21

Q1 to Q4 and Q2 to Q3