Identites/formula Etc. Flashcards
Reciprocal identity of cosecx
1 / sinx
Reciprocal identity of secx
1 / cosx
Reciprocal identity of cotx
1 / tanx
Give a pythagorean identity with cos²x
Sin²x + Cos²x = 1
Give a pythagorean identity for sec²x
Sec²x = 1+tan²x
Give a pythagorean identity for cosec²x
Cosec²x = 1 + cot²x
Addition rule for sin(A±B)
SinAcosB ± cosAsinB
Addition rule for cos(A±B)
CosAcosB - or + sinAsinB
Addition rule for tan(A±B)
Tan(A±B) = tanA ± tanB / 1 - or + tanAtanB
Sin2A double angle formula
2sinAcosA
Cos2a double angle formula
Cos²A - sin²A
Or
2cos²A - 1
Or
1 - 2sin²A
Tan2a double angle formula
2tanA / 1 - tan²A
Equation for working out arc length of a sector
S = rtheta
Equation for workout out sector area
A = (1/2)r²(theta)
Give the small angle approximation for sin(theta)
Theta
Give the small angle approximation for cos(theta)
1 - (1/2)(theta)²
Give the small angle approximation for tan(theta)
Theta
Equation to work out the distance between 2 coords
D = root((2nd x - 1st x)² + (2nd y - 1st y)²)
Gradient between 2 coords
(2nd y - 1st y) / (2nd x - 1st x)
Cosine rule
a² = b² + c² -2bcCosA
You can use this rule when:
You know all 3 sides
You know 2 sides and the angle between them
Cosine rule angle version
CosA = (b² + c² - a²) / 2bc
Give the sine rule
a / sinA = b/sinB = c / sinC
Can also be flipped aswell
Can be used if:
You know two angles and a side
Can sometimes be used if you know two sides and an angle that isn’t between them
f(2x)
horizontal
stretch of 1/2
f(x - 30)
30 right
f(x + 30)
30 left
Domain
Range of X values
Range
Range of y values
Draw cosx graph
Draw tanx graph
Draw sinx graph
2f(x)
vertical stretch of 2
÷1/2
Draw cosec graph
Draw cot graph
Draw sec graph
Formula for finding a number in a geometric sequence
ar^n-1
Formula for finding the sum of a geometric series
Sn = a(r^n - 1) / r - 1
How to find r in a geometric series
U2 /u1
Formula for sum of all values arithmetic series
Sn = n/2 ( 2a + (n-1)d)
Formula for finding a value in an arithmetic sequence
a + (n-1)d
Binomial theorem
2 different formulas for e.g. exponent of 1/2 and 2
Area
A = 1/2 absinC
Input for inverse e.g. f^-1(7) is the output for ….
Original function
f(-x)
Reflects in y axis
-f(x)
Reflects in x axis
|f(x)|
Reflects in x axis
f(|x|)
Reflects in y axis
What types of mappings on graphs are functions
Many to one
Many to many
What types of mappings on graphs aren’t functions
One to many
One to one
How can you tell a graph can have an inverse function
When you inverse the graph, if it becomes:
Many to one
Many to many
It can have an inverse
What is the inverse of a Many to one graph
One to many
