Pythagorean identities

Trigonometry Ratios-Mnemonics

• Students often use mnemonics to remember facts and relationships in trigonometry.
• For example, the sine, cosine, and tangent ratios in a right triangle can be remembered by representing them as strings of letters, as in SOH-CAH-TOA.
  Sine = Opposite ÷ Hypotenuse
  Cosine = Adjacent ÷ Hypotenuse
  Tangent = Opposite ÷ Adjacent
• Alternatively, one can devise sentences which consist of words beginning with the letters to be remembered.
• For example, to recall that Tan = Opposite/Adjacent, the letters T-O-A must be remembered. Any memorable phrase constructed of words beginning with the letters T-O-A will serve.
  
• Another type of mnemonic describes facts in a simple, memorable way, such as "Plus to the right, minus to the left; positive height, negative depth," which refers to trigonometric functions generated by a revolving line.

SET LANGUAGE

Operations on Sets
1. Union of sets : A U B = {x / x є A or x є B or x є A and x є B }
Note:
A U A = A
A n A = A
A n A’= {}
A U A’= U
2. Intersection of sets: A n B = {x / x є A and x є B }
Properties of set difference
1. Set difference is not commutative A – B ≠ B – A
2. Set difference is not associative A– (B – C) ≠ (A – B) – C
Distributive Property
1. Union is distributed over intersection A U (B n C) = (A U B ) n (AU C)
2. Intersection is distributed over union A n ( B U C) = (A n B) U (A n C)
DE Morgan’s Laws
1. Regarding complementation
(i) (A U B)’ = A’ n B’
(ii) (A n B)’ = A’ U B’
2. Regarding set difference
(i) A – (B U C) = (A – B) n (A – C)
(ii) A – (B n C) = (A – B) U (A – C)
♦ n(A U B) = n (A) + n (B) – n(A n B) if A n B ≠ { }
♦ n(A U B) = n (A) + n (B) if A n B = { }

• n(A U B U C) = n (A) + n (B) + n (C)–n(A n B)–n(B n C)–n(A n C) + n(A n B n C)