Formulas - Last units before final

Question 1

Right triangle Trigonometry

Answer 1

All angles in a triangle add to 180º
a² + b² = c²

sinθ = O/H
cscθ = H/O

cosθ = A/H
secθ = H/A

tanθ = O/A
cotθ = A/O

solve for trig functions or missing angles and sides using trig identities, resort to pythagorean theorem last

Question 2

Sine Law

Answer 2

sinA/a = sinB/b = sinC/c

Question 3

Cosine Laws

Answer 3

a² = b² + c² - 2bc * cosA
b² = a² + c² - 2ac * cosB
c² = a² + b² - 2ab * cosC

cosA = ( b² + c² - a² ) / 2bc
cosB = ( a² + c² - b² ) / 2ac
cosC = ( a² + b² - c² ) / 2ab

Question 4

Polar coordinates

Answer 4

(r, θ)

r - radius
θ - angle between horizontal and radius

Question 5

Polar coordinate to rectangular coordinate equations

Answer 5

r² = x² + y²
x = rcosθ
y = rsinθ

Question 6

Polar coordinate graphing

Answer 6

multiply both sides of equation by r to solve

if radius in negative take radius through origin to negative, negative coordinates

for graphing:
1. multiply both sides by r
2. complete the square
3. determine circle centre and radius
4. graph

Question 7

Equation of ellipse

Answer 7

If ellipse is horizontally elongated:
x²/a² + y²/b² = 1
vertices: V1(a, 0) and V2(-a, 0)

If ellipse is vertically elongated:
x²/b² + y²/a² = 1
vertices: V1(0, a) and V2(0, -a)

a² = b² + c²

a and -a are the vertices
b and -b are the points of intersection on the narrower sides of the ellipse
c and -c are the foci (found with a right angle where a is the hypotenuse equated to the length a)