Stitz-Zeager_College_Algebra_e-book

26 is a direct consequence of the facts that f x cosx

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Unformatted text preview: erminal, as are β and β0 , it follows that α − β is coterminal with α0 − β0 . Consider the case below where α0 ≥ β0 . y y 1 P (cos(α0 ), sin(α0 )) α0 − β0 A(cos(α0 − β0 ), sin(α0 − β0 )) Q(cos(β0 ), sin(β0 )) α0 α0 − β 0 β0 O 1 x O B (1, 0) x Since the angles P OQ and AOB are congruent, the distance between P and Q is equal to the distance between A and B .2 The distance formula, Equation 1.1, yields (cos(α0 ) − cos(β0 ))2 + (sin(α0 ) − sin(β0 ))2 = (cos(α0 − β0 ) − 1)2 + (sin(α0 − β0 ) − 0)2 Squaring both sides, we expand the left hand side of this equation as (cos(α0 ) − cos(β0 ))2 + (sin(α0 ) − sin(β0 ))2 = cos2 (α0 ) − 2 cos(α0 ) cos(β0 ) + cos2 (β0 ) + sin2 (α0 ) − 2 sin(α0 ) sin(β0 ) + sin2 (β0 ) = cos2 (α0 ) + sin2 (α0 ) + cos2 (β0 ) + sin2 (β0 ) −2 cos(α0 ) cos(β0 ) − 2 sin(α0 ) sin(β0 ) From the Pythagorean Identities, cos2 (α0 ) + sin2 (α0 ) = 1 and cos2 (β0 ) + sin2 (β0 ) = 1, so 2 In the picture we...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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