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# 0712 ch 7 day 12

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• ### 0712 ch 7 day 12

1. 1. 7.5 Trigonometric Equations Day TwoIsaiah 33:2O LORD, be gracious to us; we long for you. Be our strengthevery morning, our salvation in time of distress.
2. 2. 8. Groups: Find all solutions of: 2 2sin θ − sin θ − 1 = 0
3. 3. 8. Groups: Find all solutions of: 2 2sin θ − sin θ − 1 = 0 using Quadratic Formula program: 1 sin θ = 1 sin θ = − 2 π 7π 11π θ= θ= , 2 6 6 π 7π 11π θ = + 2kπ , + 2kπ , + 2kπ 2 6 6
4. 4. 9. Groups: Solve graphically for −π ≤ x ≤ π 1.05sin x − 1.07 = 0
5. 5. 9. Groups: Solve graphically for −π ≤ x ≤ π 1.05sin x − 1.07 = 0 ∅
6. 6. 9. Groups: Solve graphically for −π ≤ x ≤ π 1.05sin x − 1.07 = 0 ∅ Discuss how this could have been obtained without graphing.
7. 7. 10. Groups: Find all solutions in 0 ≤ θ < 2π 2 8sin θ − 5sin θ − 1 = 0
8. 8. 10. Groups: Find all solutions in 0 ≤ θ < 2π 2 8sin θ − 5sin θ − 1 = 0 sin θ ≈ .7844 sin θ ≈ −.1594
9. 9. 10. Groups: Find all solutions in 0 ≤ θ < 2π 2 8sin θ − 5sin θ − 1 = 0 sin θ ≈ .7844 sin θ ≈ −.1594 θ ≈ .90 QI
10. 10. 10. Groups: Find all solutions in 0 ≤ θ < 2π 2 8sin θ − 5sin θ − 1 = 0 sin θ ≈ .7844 sin θ ≈ −.1594 θ ≈ .90 QI θ ≈ π − .90
11. 11. 10. Groups: Find all solutions in 0 ≤ θ < 2π 2 8sin θ − 5sin θ − 1 = 0 sin θ ≈ .7844 sin θ ≈ −.1594 θ ≈ .90 QI θ ≈ π − .90 θ ≈ 2.24 QII
12. 12. 10. Groups: Find all solutions in 0 ≤ θ < 2π 2 8sin θ − 5sin θ − 1 = 0 sin θ ≈ .7844 sin θ ≈ −.1594 θ ≈ .90 QI θ ≈ −.16 θ ≈ π − .90 θ ≈ 2.24 QII
13. 13. 10. Groups: Find all solutions in 0 ≤ θ < 2π 2 8sin θ − 5sin θ − 1 = 0 sin θ ≈ .7844 sin θ ≈ −.1594 θ ≈ .90 QI θ ≈ −.16 θ ≈ π − .90 ∴ θ ≈ 2π − .16 θ ≈ 2.24 QII
14. 14. 10. Groups: Find all solutions in 0 ≤ θ < 2π 2 8sin θ − 5sin θ − 1 = 0 sin θ ≈ .7844 sin θ ≈ −.1594 θ ≈ .90 QI θ ≈ −.16 θ ≈ π − .90 ∴ θ ≈ 2π − .16 θ ≈ 2.24 QII θ ≈ 6.12 QIV
15. 15. 10. Groups: Find all solutions in 0 ≤ θ < 2π 2 8sin θ − 5sin θ − 1 = 0 sin θ ≈ .7844 sin θ ≈ −.1594 θ ≈ .90 QI θ ≈ −.16 θ ≈ π − .90 ∴ θ ≈ 2π − .16 θ ≈ 2.24 QII θ ≈ 6.12 QIV θ ≈ π + .16
16. 16. 10. Groups: Find all solutions in 0 ≤ θ < 2π 2 8sin θ − 5sin θ − 1 = 0 sin θ ≈ .7844 sin θ ≈ −.1594 θ ≈ .90 QI θ ≈ −.16 θ ≈ π − .90 ∴ θ ≈ 2π − .16 θ ≈ 2.24 QII θ ≈ 6.12 QIV θ ≈ π + .16 θ ≈ 3.30 QIII
17. 17. 10. Groups: Find all solutions in 0 ≤ θ < 2π 2 8sin θ − 5sin θ − 1 = 0 sin θ ≈ .7844 sin θ ≈ −.1594 θ ≈ .90 QI θ ≈ −.16 θ ≈ π − .90 ∴ θ ≈ 2π − .16 θ ≈ 2.24 QII θ ≈ 6.12 QIV θ ≈ π + .16 θ ≈ 3.30 QIII {.90, 2.24, 3.30, 6.12}
18. 18. HW #10 Quiz Tomorrow!!Happiness is not in the mere possession of money; it liesin the joy of achievement, in the thrill of creativeeffort. Franklin D. Roosevelt