Mathematics

Formulas: Chap.19, chap.20, chap.24, chap.25

Sin ( θ )

Opp / Hyp

Cos ( θ )

Adj / Hyp

Tan ( θ )

Opp / Adj, sin ( θ ) / cos ( θ )

Right-angled Triangle

A: hypothenuse

B: adjacent

C: opposite

Angles

A: Angle of elevation

B: Angle of depression

Cos ( θ ) rule supplementary

Cos ( 180 - θ ) = - cos ( θ )

Sin ( θ ) rule supplementary

Sin ( 180 - angle ) = sin ( angle )

Area of a non-right angled triangle

½ ab sin ( C )

Cosine rule ( a )

a² = b² + c² - 2bc cos ( A )

Function

A relation where no two pairs share the same x

Relation

Any set of ( x, y )

Function Notation

f (x) = rule

Domain in set builder notation

{ x | … }

Range

{ y | … }

Shift up

y = f( x ) + k

Shift right

y = f( x - k )

Shift left

y = f( x + k )

Reflect in the x axis

y = - f( x ) ( vertical reflection )

Reflect in the y axis

y = f( - x ) ( horizontal reflection )

Axis of symmetry ( 1 )

x = -b / 2a

Maximum or minimum parabola

a over 0 ( minimum ), a under 0 ( maximum )

Root equation

root = b² - 4ac

Intercepts from root

root over 0 ( 2 ), root equal to 0 ( 1 ), root under 0 ( 0 )

Vertex form

f ( x ) = a ( x - h )² + k

Factored form

f ( x ) = a ( x - p )( x - q )

p

x intercept 1

q

x intercept 2

h

vertex x

k

vertex y

Axis of symmetry ( 2 )

x = p + q / 2

Integers

Whole numbers with no fractions / decimals ( -3, -2, -1, 0, 1, 2, 3, etc. )

Rational numbers

Any number that can be expressed as a function ( - 1/2, 2/3, 4/1, etc. )

Interval notation

( starting point, endpoint ) ( left, right )/( bottom, top )

Interval notation (

Excludes

Interval notation [

Includes

Sine rule

a / sin A = b / sin B = c / sin C

Triangle area equation ( non right angled )

½ ab sin c

Cosine rule ( A )

Cos A = b²+c²-a² / 2bc

sin ( θ ) complementary rule

cos ( 90 - angle ) = sin ( angle )

cos ( θ ) complementary rule

sin ( 90 - angle ) = cos ( angle )