ch.9 Trigonometric Identities and Their Applications

ch.9 Trigonometric Identities and Their Applications -...

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Chapter 9 Trigonometric Identities and Their Applications 9.1 Identities, Expressions and Equations
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Key Points The difference between an equation and an identity The Pythagorean and double angle identities
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Identities (8, 16) Pythagorean Quotient 2 2 2 2 2 2 sin cos 1, tan 1 sec , 1 cot csc θ + = + = + = sin tan cos cos cot sin = =
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Double-Angle Identities 2 2 2 2 2 cos2 cos sin cos2 1 2sin cos2 2cos 1 sin 2 2sin cos 2tan tan 2 1 tan A A A A A A A A A A A A A = - = - = - = = -
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Using Identities to Solve Equations Example 7 Find all solutions to the equation sin 2 t = 2 sin t on the interval 0 ≤ t ≤ 2π. Functions Modeling Change: A Preparation for Calculus, 4th
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Using Identities to Solve Equations Functions Modeling Change: A Preparation for Calculus, 4th y = sin 2 t y = 2 sin t
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Hints for Verifying Identities 1. Learn the fundamental identities given in the last section. Whenever you see either side of a fundamental identity, the other side should come to mind. Also, be aware of equivalent forms of the fundamental identities. For example is an alternative form of the identity 2. Try to rewrite the more complicated side of the equation so that it is identical to the simpler side. 2 2 sin 1 cos θ = - 2 2 sin cos 1. + =
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Hints for Verifying Identities continued 3. It is sometimes helpful to express all trigonometric functions in the equation in terms of sine and cosine and then simplify the result. 4.
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This note was uploaded on 04/04/2012 for the course MATH 2412 taught by Professor Staff during the Spring '08 term at Austin CC.

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ch.9 Trigonometric Identities and Their Applications -...

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