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November 5, 2012 Using Fundamental Identities

November 5, 2012 Using Fundamental Identities. Warm-up: Find the trig value for: sec(11π/6) 2. cot(2π/3) 3. csc(2π) Find the angle θ for: 4. tanθ = -√3 5. 6. cotθ = -1. CW/HW 5.1: Pg. 379 #15-43, 45-53 Odds only. Derive the three Pythagorean Identities.

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November 5, 2012 Using Fundamental Identities

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  1. November 5, 2012Using Fundamental Identities Warm-up: Find the trig value for: • sec(11π/6) 2. cot(2π/3) 3. csc(2π) Find the angle θ for: 4. tanθ = -√3 5. 6. cotθ = -1 CW/HW 5.1: Pg. 379 #15-43, 45-53 Odds only

  2. Derive the three Pythagorean Identities sin2θ + cos2θ = 1 1 + tan2θ = sec2θ 1 + cot2θ = csc2θ

  3. Lesson 5.1Using Fundamental Trig Identities Reciprocal Identities Quotient Identities Pythagorean Identities 1+ tan2θ = sec2θ sin2θ + cos2θ = 1 1+ cot2θ = csc2θ

  4. Cofunction Identities

  5. Verify one of the cofunction identitiesShow that Take a look at a 30-60-90 triangle 30° 2 √3 60° 1 ✓

  6. Negative Angle Identities Show that these identities are true. Use any angle for θ.

  7. Simplifying an expressions to get a single value. The goal is to use the identities to substitute and simplify. You want to try to get a single term. Example 1: Transform the left side of the equation into the right side (0 < θ < π/2) • tanθcotθ = 1 b) cotθsinθ = cosθ

  8. More simplifyingTry to rewrite as a single term Example 2: a) b) c)

  9. Start practicing on HWPg. 379 #15-43

  10. Use factoring to simplify Example 3: common factordifference of squares • sin2x csc2x – sin2x b) sec4x – tan4x Use these strategies for HW #45-53 odd

  11. All the Trig Identities:

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