Identites/formula Etc.

Question 1

Reciprocal identity of cosecx

Answer 1

1 / sinx

Question 2

Reciprocal identity of secx

Answer 2

1 / cosx

Question 3

Reciprocal identity of cotx

Answer 3

1 / tanx

Question 4

Give a pythagorean identity with cos²x

Answer 4

Sin²x + Cos²x = 1

Question 5

Give a pythagorean identity for sec²x

Answer 5

Sec²x = 1+tan²x

Question 6

Give a pythagorean identity for cosec²x

Answer 6

Cosec²x = 1 + cot²x

Question 7

Addition rule for sin(A±B)

Answer 7

SinAcosB ± cosAsinB

Question 8

Addition rule for cos(A±B)

Answer 8

CosAcosB - or + sinAsinB

Question 9

Addition rule for tan(A±B)

Answer 9

Tan(A±B) = tanA ± tanB / 1 - or + tanAtanB

Question 10

Sin2A double angle formula

Answer 10

2sinAcosA

Question 11

Cos2a double angle formula

Answer 11

Cos²A - sin²A

Or

2cos²A - 1

Or

1 - 2sin²A

Question 12

Tan2a double angle formula

Answer 12

2tanA / 1 - tan²A

Question 13

Equation for working out arc length of a sector

Answer 13

S = rtheta

Question 14

Equation for workout out sector area

Answer 14

A = (1/2)r²(theta)

Question 15

Give the small angle approximation for sin(theta)

Answer 15

Theta

Question 16

Give the small angle approximation for cos(theta)

Answer 16

1 - (1/2)(theta)²

Question 17

Give the small angle approximation for tan(theta)

Answer 17

Theta

Question 18

Equation to work out the distance between 2 coords

Answer 18

D = root((2nd x - 1st x)² + (2nd y - 1st y)²)

Question 19

Gradient between 2 coords

Answer 19

(2nd y - 1st y) / (2nd x - 1st x)

Question 20

Cosine rule

Answer 20

a² = b² + c² -2bcCosA

You can use this rule when:
You know all 3 sides

You know 2 sides and the angle between them

Question 21

Cosine rule angle version

Answer 21

CosA = (b² + c² - a²) / 2bc

Question 22

Give the sine rule

Answer 22

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

Question 23

f(2x)

Answer 23

horizontal
stretch of 1/2

Question 24

f(x - 30)

Answer 24

30 right

Question 25

f(x + 30)

Answer 25

30 left

Question 26

Domain

Answer 26

Range of X values

Question 27

Range

Answer 27

Range of y values

Question 28

Draw cosx graph

Question 29

Draw tanx graph

Question 30

Draw sinx graph

Question 31

2f(x)

Answer 31

vertical stretch of 2 ÷1/2

Question 32

Draw cosec graph

Question 33

Draw cot graph

Question 34

Draw sec graph

Question 35

Formula for finding a number in a geometric sequence

Answer 35

ar^n-1

Question 36

Formula for finding the sum of a geometric series

Answer 36

Sn = a(r^n - 1) / r - 1

Question 37

How to find r in a geometric series

Answer 37

U2 /u1

Question 38

Formula for sum of all values arithmetic series

Answer 38

Sn = n/2 ( 2a + (n-1)d)

Question 39

Formula for finding a value in an arithmetic sequence

Answer 39

a + (n-1)d

Question 40

Binomial theorem

Answer 40

2 different formulas for e.g. exponent of 1/2 and 2

Question 41

Area

Answer 41

A = 1/2 absinC

Question 42

Input for inverse e.g. f^-1(7) is the output for ....

Answer 42

Original function

Question 43

f(-x)

Answer 43

Reflects in y axis

Question 44

-f(x)

Answer 44

Reflects in x axis

Question 45

|f(x)|

Answer 45

Reflects in x axis

Question 46

f(|x|)

Answer 46

Reflects in y axis

Question 47

What types of mappings on graphs are functions

Answer 47

Many to one Many to many

Question 48

What types of mappings on graphs aren't functions

Answer 48

One to many One to one

Question 49

How can you tell a graph can have an inverse function

Answer 49

When you inverse the graph, if it becomes: Many to one Many to many It can have an inverse

Question 50

What is the inverse of a Many to one graph

Answer 50

One to many