Stitz-Zeager_College_Algebra_e-book

# 2 if sin x for nd an expression for sin2 in terms

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Unformatted text preview: north latitude to be 2960 miles. Justify this approximation if the radius of the Earth at the Equator is approximately 3960 miles. Solution. 1. Using Theorem 10.3 with √ = 4 and y = −2, we ﬁnd r = x √ 25 x 4 √ that cos(θ) = r = 2√5 = 5 and y = y = 2−25 = − 55 . r (4)2 + (−2)2 = √ √ 20 = 2 5 so 2. Assuming the Earth is a sphere, a cross-section through the poles produces a circle of radius 3960 miles. Viewing the Equator as the x-axis, the value we seek is the x-coordinate of the point Q(x, y ) indicated in the ﬁgure below. y y 3960 4 Q (x, y ) 2 41.628◦ −4 −2 2 −2 4 x 3960 x Q(4, −2) −4 The terminal side of θ contains Q(4, −2) A point on the Earth at 41.628◦ N Using Theorem 10.3, we get x = 3960 cos (41.628◦ ). Using a calculator in ‘degree’ mode, we ﬁnd 3960 cos (41.628◦ ) ≈ 2960. Hence, the radius of the Earth at North Latitude 41.628◦ is approximately 2960 miles. 10.2 The Unit Circle: Cosine and Sine 627 Theorem 10.3 gives us what we need to describe the position of an object traveling in a circula...
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