Pythagoras, Trigonometry and Sets

Question 1

What does A⊄B mean?

Answer 1

A is not a subset of B

Question 2

What does ∉ mean?

Answer 2

It means “is not an element of”. If an element e does not belongs to a set S then we write e ∉ S (e is not an element of S)

Question 3

How do you work out the hypotenuse of a triangle?

Answer 3

Tangent = opposite/adjacent

Question 4

What is the Hypotenuse?

Answer 4

The longest side of the triangle (opposite the right angle)

Question 5

How do you work out the length of a side (Y) when only 1 side is given and angle X (denominator unknown)?

Answer 5

1st. You figure out if your using sin/cos/tan with the given side (eg 7) and Y
2nd. You put the given angle in the brackets - eg tan(43) - then you write the sides as a fraction - eg tan(43)=7/X
3rd. The tan(43) and the X swap - eg X=7/tan(43)
4th. On your calculator type in 7/tan(43) to work out the missing side

Question 6

What is sine, cosine and tangent?

Answer 6

Ratios used in trigonometry to find out a side or an angle of a triangle

Question 7

What does Ø mean?

Answer 7

An empty set

Question 8

How do you work out the adjacent side of a triangle?

Answer 8

Sine = opposite/hypotenuse

Question 9

What is a set?

Answer 9

A set is a well defined group of objects which can be finite or infinite

Question 10

What does A⊂B mean?

Answer 10

A is a subset of B

Question 11

What is the adjacent side?

Answer 11

The side next to the angle X

Question 12

What is the opposite side?

Answer 12

The side opposite to the angle X

Question 13

What is an element?

Answer 13

The members of the set are called elements “e”.

Question 14

What does∈mean?

Answer 14

It means “is an element of”. If an element e belongs to a set S then we write e∈S (e is an element of S)

Question 15

What does n(S) mean?

Answer 15

The number of elements of a set can be written as n(S)=no. of elements

Question 16

Ηοw do you work out the missing X angle using trigonometry?

Answer 16

1st. You figure out if your using sin/cos/tan with the given sides
2nd. You use the -1 sign with the ratio your using (bare in mind the -1 is small) with the fraction you have made with the side lengths- tan-1(6/7)
3rd. To get the -1 ratio you have to press shift then on the ratio.
4th. Type tan-1(6/7) in your calculator to get the answer

Question 17

What is SOHCAHTOA?

Answer 17

A way to remember which ratio you need to use with which sides: 
Sine
Opposite
Hypotenuse 
Cosine 
Adjacent 
Hypotenuse 
Tangent
Opposite 
Adjacent

Question 18

How do you work out the length of a side (Y) when only 1 side is given and angle X (numerator unknown)?

Answer 18

1st. You figure out if your using sin/cos/tan with the given side (eg 7) and Y
2nd. You put the given angle in the brackets - eg tan(43) - then you times it by the given side - eg tan(43) x 7 (= Y)
3rd. On your calculator type in tan(43) x 7 to work out the missing side

Question 19

List all the subsets of set A consisting of these 3 fruits, apple, peach and mango

A={Apple, peach, mango}

Answer 19

{apple}
{peach} 
{mango}
{apple,peach}
{apple,mango}
{mango,peach}
{apple,mango,peach}
Ø

Question 20

What are { }?

Answer 20

They are braces which contain the elements of a set

Question 21

What are compliments?

Answer 21

You define the compliment by putting a dash infront of the set letter and in the braces elements that are not in in that particular subset but in the universal set

Question 22

What is rounding?

Answer 22

Making a number easier to work with by giving less digits

Question 23

List the common types of Venn diagrams.

Answer 23

• two circles overlapping
• one circle inside another
• three circles overlapping
• two circles by themselves

Question 24

What does ∪ mean?

Answer 24

It is the union and it is all the elements that appear in two or more sets

Question 25

What are Venn diagrams?

Answer 25

Venn diagrams are a way of showing sets in a diagram. The universal set is represented by a rectangle and subsets are shown in circles within the rectangle.

Question 26

How do you work out the opposite side of the triangle?

Answer 26

Cosine = adjacent/hypotenuse

Question 27

What are universal sets?

Answer 27

The universal set is the set that contains all elements for a particular problem. This set can be denoted by the letter E (which is curly).

Question 27

What are significant figures?

Answer 27

The number of digits after the first non-zero digit

Question 29

what does ∩ mean?

Answer 29

It is the intersection and it is the elements that are common to two or more sets

Question 30

What are decimal places?

Answer 30

The number of digits after the decimal point

Question 31

How do you write the missing X angle answer?

Answer 31

θ = (missing X angle)