Unformatted text preview: ) = cos(4θ).
2. Identifying α = θ and β = 3θ yields
θ − 3θ
θ + 3θ
cos
2
2
= 2 sin (−θ) cos (2θ)
= −2 sin (θ) cos (2θ) , sin(θ) − sin(3θ) = 2 sin where the last equality is courtesy of the odd identity for sine, sin(−θ) = − sin(θ). 10.4 Trigonometric Identities 667 The reader is reminded that all of the identities presented in this section which regard the circular
functions as functions of angles (in radian measure) apply equally well to the circular functions
regarded as functions of real numbers. In Section 10.5, we see how some of these identities manifest
themselves geometrically as we study the graphs of the trigonometric functions. 668 Foundations of Trigonometry 10.4.1 Exercises 1. Verify the Even / Odd Identities for tangent, secant, cosecant and cotangent.
2. Use the Even / Odd Identities to verify the following identities. Assume all quantities are
deﬁned.
(d) csc(−t − 5) = − csc(t + 5) (a) sin(3π − 2t) = − sin(2t − 3π )
π
π
(b) cos − − 5t = cos 5...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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