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

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

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

4. Cofunction Identities

5. Verify one of the cofunction identities Show that
Take a look at a 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)
tanθ cotθ = 1 b) cotθ sinθ = cosθ

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

9. Start practicing on HW Pg. 379 #15-43

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

11. All the Trig Identities: