The document discusses Pythagorean identities. It introduces the Pythagorean theorem that relates the sides of a right triangle, and defines trigonometric functions in terms of angles. It then lists four fundamental Pythagorean identities: 1) sin2θ + cos2θ = 1, 2) 1 + tan2θ = sec2θ, 3) cot2θ + 1 = csc2θ, and 4) sec2A - 1 = csc2A tan2A. It provides examples and homework problems related to these identities.

1. Aim: What are the Pythagorean Identities? MB43 12/3/08 Lomas Do Now: Name the reciprocal identities we talked about yesterday Name the quotient identities we talked about yesterday HW Review: 3, 7, 12 HW: Read 680-683 Do pg 684 #15-35odd

2. Aim: What are the Pythagorean Identities? MB43 12/3/08 Lomas 1 y x (x,y) Pythagorean Theorem says x 2 +y 2 =1 and we know that x = cos θ and y = sin θ θ HW: Read 680-683 Do pg 684 #15-35odd

3. Aim: What are the Pythagorean Identities? MB43 12/3/08 Lomas sin 2 θ + cos 2 θ = 1 HW: Read 680-683 Do pg 684 #15-35odd

4. Aim: What are the Pythagorean Identities? MB43 12/3/08 Lomas Pythagorean Identities: sin 2 θ + cos 2 θ = 1 1 + tan 2 θ = sec 2 θ cot 2 θ + 1 = csc 2 θ HW: Read 680-683 Do pg 684 #15-35odd

5. Aim: What are the Pythagorean Identities? MB43 12/3/08 Lomas If sec A = -3 and <A is in Quad II find tan A Express 1 + cot 2 θ in terms of sine and cosine or both HW: Read 680-683 Do pg 684 #15-35odd

6. Aim: What are the Pythagorean Identities? MB43 12/3/08 Lomas csc A tan A sec 2 A - 1 HW: Read 680-683 Do pg 684 #15-35odd

7. Aim: What are the Pythagorean Identities? MB43 12/3/08 Lomas HW: Read 680-683 Do pg 684 #15-35odd