Some Math

Trig

100

sin(30º)

0.5

200

cos(a) = ?

a/h

300

tan(a) = ?

(using trig functions)

sin/cos

500

Area of a Triangle using sines and cosines

a*b*sin(c)/2

1000

CALCULATORS ALLOWED:

Given △ABC, AC = 12, AB = CB = 10.

Find ∠A, ∠B, ∠C (Approx.)

A: 53.13º, B: 73.74º, C: 53.13º.

Theorems

100

1+2+3+4+...+n?

(n+1)(n)/2

200

Pythagorean theorem

a²+b²=c²

300

Euler's theorem

e^i∏ + 1 = 0

500

Solve: Ax²+Bx+C=0

x = (-B±√B̅²-̅4̅A̅C̅)/2A

1000

Law of cosines

c²=a²+b²-2ab*cos(C)

Inequalities

100

3x > 0

x > 0

200

x²+3x+2 ≥ 0

x ≤ -2, x ≥ -1

300

(3x+1)/(2x-1) > 0

x < -1/3, x > 1/2

500

2x²+1 > 0

x∈ℝ

1000

(3+x)²(x-2)³(5-x)⁴

----------------------   ≥ 0

(32+x)³(30+x)²(x²+1)

x ≥ 2, x < -32, x = -3

Names of symbols

100

∏

Pi = 3.14159...

200

e

e = 2.7186...

300

θ

θ = An angle

500

∑

Summation

1000

ℵ₀

Aleph-null, countable infinity

Triangles

100

Sum of angles

180º

200

Triangle inequality 1

a ≥ b+c

300

Triangle inequality 2

The biggest angle is across from the longest side

500

30 60 90 triangle sides ratio

a:b:c

√3:1:2

1000

Prove Triangles 100.

If you make parallel lines, one on the point of the triangle and one on the segment below, you can use theorems to prove.