Equations/Laws

Question 1

Sine rule

Answer 1

a/sinA = b/sinB = c/ sinC

Question 2

Cosine rule (side)

Answer 2

a² = b² + c² - 2abCosA

Question 3

Cosine rule (angle)

Answer 3

CosA = (c² + b² - a²) / 2ab

Question 4

Discriminant

Answer 4

b² - 4ac

Question 5

Quadratic formula

Answer 5

x = (−b ± √(b² − 4ac)) / 2a

Question 6

Logarithms Laws

Answer 6

1. logₐ(xy) = logₐ(x) + logₐ(y)
2. logₐ(x/y) = logₐ(x) − logₐ(y)
3. logₐ(xⁿ) = n·logₐ(x)
4. logₐ(a) = 1
5. logₐ(1) = 0
6. If logₐ(x) = logₐ(y), then x = y
7. Change of base: logₐ(x) = log_b(x) / log_b(a) (common bases: b = 10 or e)

Question 7

Area of a triangle

Answer 7

½abSinC

Question 8

Exact trig values for Sine

Answer 8

Sin 0 = 0
Sin 30 = ½
Sin 45 = √2/2
Sin 60 = √3/2

Question 9

Exact trig values for cos

Answer 9

Cos 0 = 1
Cos 30 = √3/2
Cos 45 = √2/2
Cos 60 = ½

Question 10

Exact trig values for tan

Answer 10

Tan 0 = 0
Tan 30 = √3/3
Tan 45 = 1
Tan 60 = √3
Tan 90 = undefined

Question 11

Trig identities

Answer 11

Tan θ = Sin θ / Cos θ
Sin²θ + cos²θ = 1