TRIGONOMETRY – ADVANCED FORMULAS
DOUBLE ANGLE FORMULAS
Sin2A = 2 sinA cosA
cos 2A = 1 – 2 sin2A
cos 2A = 2 cos2A -1
TRIPLE ANGLE FORMULAS
sin 3A = 3 sinA – 4 sin3 A
cos 3A = 4 cos3A – 3 cosA
PRODUCT TO SUM FORMULAS
sinA sinB = [cos(A-B) – cos(A+B)]
cosA cosB = [cos(A-B) + cos(A+B)]
sinA cosB = [sin(A+B) + sin(A-B)]
SUM TO PRODUCT FORMULAS
MAXIMUM & MINIMUM VALUES
a sin ø + b cosø = = a2
b2
Maximum value = a2
b2
Minimum value = a2
b2
SIMPLE INTEREST – FORMULAS & CONCEPTS
BASIC TERMS
Principal (P) Amount borrowed or invested
Rate (R) Rate of interest per year
Time (T) Time in years
SIMPLE INTEREST FORMULA
SI =
AMOUNT FORMULA
Amount (A) = P + SI
VARIATIONS
P =
R =
T=
TIME CONVERSION
Months
divide by 12
Days
divide by 365
QUICK TIPS
SI is always calculated on Principal
Rate remains same every year
PERCENTAGE – FORMULAS & SHORT TRICKS
BASIC DEFINITION
Percentage =
100
PERCENT CONVERSION
x% =
1% =
INCREASE & DECREASE ·
Increase % =
× 100
Decrease % =
× 100
SUCCESSIVE CHANGE
Net % change = a + b +
IMPORTANT EQUIVALENTS
10% = 1/10
20% = 1/5
25% = 1/4
50% = 1/2
QUICK TIPS
x% of y = y% of x
To find 10%
divide by 10