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Pre-Calc Exam Notes 70

# Pre-Calc Exam Notes 70 - 70 Chapter 3 Identities 3.1...

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70 Chapter 3 Identities §3.1 Exercises 1. We showed that sin θ = ± radicallow 1 cos 2 θ for all θ . Give an example of an angle θ such that sin θ = − radicallow 1 cos 2 θ . 2. We showed that cos θ = ± radicalbig 1 sin 2 θ for all θ . Give an example of an angle θ such that cos θ = − radicalbig 1 sin 2 θ . 3. Suppose that you are given a system of two equations of the following form: 1 A cos φ = B ν 1 B ν 2 cos θ A sin φ = B ν 2 sin θ . Show that A 2 = B 2 ( ν 2 1 + ν 2 2 2 ν 1 ν 2 cos θ ) . For Exercises 4-16, prove the given identity. 4. cos θ tan θ = sin θ 5. sin θ cot θ = cos θ 6. tan θ cot θ = tan 2 θ 7. csc θ sin θ = csc 2 θ 8. cos 2 θ 1 + sin θ = 1 sin θ 9. 1 2 cos 2 θ sin θ cos θ = tan θ cot θ 10. sin 4 θ cos 4 θ = sin 2 θ cos 2 θ 11. cos 4 θ sin 4 θ = 1 2 sin 2 θ 12. 1 tan θ 1 + tan θ = cot θ 1 cot θ + 1 13. tan θ + tan φ cot θ + cot φ = tan θ tan φ 14.
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