Stitz-Zeager_College_Algebra_e-book

4 c the number t arccos 2 2 lies in the interval

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Unformatted text preview: ve drawn, the triangles P OQ and AOB are congruent, which is even better. However, α0 − β0 could be 0 or it could be π , neither of which makes a triangle. It could also be larger than π , which makes a triangle, just not the one we’ve drawn. You should think about those three cases. 10.4 Trigonometric Identities 657 (cos(α0 ) − cos(β0 ))2 + (sin(α0 ) − sin(β0 ))2 = 2 − 2 cos(α0 ) cos(β0 ) − 2 sin(α0 ) sin(β0 ) Turning our attention to the right hand side of our equation, we find (cos(α0 − β0 ) − 1)2 + (sin(α0 − β0 ) − 0)2 = cos2 (α0 − β0 ) − 2 cos(α0 − β0 ) + 1 + sin2 (α0 − β0 ) = 1 + cos2 (α0 − β0 ) + sin2 (α0 − β0 ) − 2 cos(α0 − β0 ) Once again, we simplify cos2 (α0 − β0 ) + sin2 (α0 − β0 ) = 1, so that (cos(α0 − β0 ) − 1)2 + (sin(α0 − β0 ) − 0)2 = 2 − 2 cos(α0 − β0 ) Putting it all together, we get 2 − 2 cos(α0 ) cos(β0 ) − 2 sin(α0 ) sin(β0 ) = 2 − 2 cos(α0 − β0 ), which simplifies to: cos(α0...
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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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