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Stitz-Zeager_College_Algebra_e-book

# 6 2 alternatively we could have extended the graph of

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Unformatted text preview: which, when multiplied, produce a diﬀerence of squares that can be simpliﬁed to one term using one of the Pythagorean Identities in Theorem 10.8. Below is a list of the (basic) Pythagorean Conjugates and their products. Pythagorean Conjugates • 1 + cos(θ) and 1 − cos(θ): (1 + cos(θ))(1 − cos(θ)) = 1 − cos2 (θ) = sin2 (θ) • 1 + sin(θ) and 1 − sin(θ): (1 + sin(θ))(1 − sin(θ)) = 1 − sin2 (θ) = cos2 (θ) • sec(θ) + tan(θ) and sec(θ) − tan(θ): (sec(θ) + tan(θ))(sec(θ) − tan(θ)) = sec2 (θ) − tan2 (θ) = 1 • csc(θ) + cot(θ) and csc(θ) − cot(θ): (csc(θ) + cot(θ))(csc(θ) − cot(θ)) = csc2 (θ) − cot2 (θ) = 1 10.3.1 Beyond the Unit Circle In Section 10.2, we generalized the functions cosine and sine from coordinates on the Unit Circle to coordinates on circles of radius r. Using Theorem 10.3 in conjunction with Theorem 10.8, we generalize the remaining circular functions in kind. Theorem 10.9. Suppose Q(x, y ) is the point on the termin...
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