Unformatted text preview: C is acute and for when C is obtuse. In both cases, we have A ≤ C and B ≤ C . We will Frst show that sin A ≤ sin C and sin B ≤ sin C . y x r r ( x 1 , y 1 ) ( x 2 , y 2 ) A C Figure 2.1.5 If C is acute, then A and B are also acute. Since A ≤ C , imagine that A is in standard position in the xycoordinate plane and that we rotate the terminal side of A counterclockwise to the terminal side of the larger angle C , as in ±igure 2.1.5. If we pick points ( x 1 , y 1 ) and ( x 2 , y 2 ) on the terminal sides of A and C , respectively, so that their distance to the origin is the same number r , then we see from the picture that y 1 ≤ y 2 , and hence sin A = y 1 r ≤ y 2 r = sin C . By a similar argument, B ≤ C implies that sin B ≤ sin C . Thus, sin A ≤ sin C and sin B ≤ sin C when C is acute. We will now show that these inequalities hold when C is obtuse....
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 Fall '11
 Dr.Cheun
 Calculus, Angles, Law of sines, Right triangle, Sin, Hypotenuse, triangle

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