Pythagoras, Trigonometry and Sets Flashcards
(31 cards)
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
