Pythagoras, Trigonometry and Sets Flashcards
What does A⊄B mean?
A is not a subset of B
What does ∉ mean?
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)
How do you work out the hypotenuse of a triangle?
Tangent = opposite/adjacent
What is the Hypotenuse?
The longest side of the triangle (opposite the right angle)
How do you work out the length of a side (Y) when only 1 side is given and angle X (denominator unknown)?
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
What is sine, cosine and tangent?
Ratios used in trigonometry to find out a side or an angle of a triangle
What does Ø mean?
An empty set
How do you work out the adjacent side of a triangle?
Sine = opposite/hypotenuse
What is a set?
A set is a well defined group of objects which can be finite or infinite
What does A⊂B mean?
A is a subset of B
What is the adjacent side?
The side next to the angle X
What is the opposite side?
The side opposite to the angle X
What is an element?
The members of the set are called elements “e”.
What does∈mean?
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)
What does n(S) mean?
The number of elements of a set can be written as n(S)=no. of elements
Ηοw do you work out the missing X angle using trigonometry?
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
What is SOHCAHTOA?
A way to remember which ratio you need to use with which sides: Sine Opposite Hypotenuse Cosine Adjacent Hypotenuse Tangent Opposite Adjacent
How do you work out the length of a side (Y) when only 1 side is given and angle X (numerator unknown)?
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
List all the subsets of set A consisting of these 3 fruits, apple, peach and mango
A={Apple, peach, mango}
{apple}
{peach}
{mango}
{apple,peach}
{apple,mango}
{mango,peach}
{apple,mango,peach}
ØWhat are { }?
They are braces which contain the elements of a set
What are compliments?
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
What is rounding?
Making a number easier to work with by giving less digits
List the common types of Venn diagrams.
- two circles overlapping
- one circle inside another
- three circles overlapping
- two circles by themselves
What does ∪ mean?
It is the union and it is all the elements that appear in two or more sets
What are Venn diagrams?
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.
How do you work out the opposite side of the triangle?
Cosine = adjacent/hypotenuse
What are universal sets?
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).
What are significant figures?
The number of digits after the first non-zero digit
what does ∩ mean?
It is the intersection and it is the elements that are common to two or more sets
What are decimal places?
The number of digits after the decimal point
How do you write the missing X angle answer?
θ = (missing X angle)
