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Unformatted text preview: of conservation of momentum.) Show that T / 2 turns sin( x ) into cos( x ). Answer: Using various standard trig manipulations, [1, pp. 43-44]: T / 2 sin( x ) = sin p x + 1 2 P = cos( x ) = cos( x ) . Or just compare the graphs visually, [1, p. 43]. 2.4.4 Solution mathops-d Question: The inversion operator Inv turns f ( x ) into f ( x ). It plays a part in the question to what extent physics looks the same when seen in the mirror. Show that Inv leaves cos( x ) unchanged, but turns sin( x ) into sin( x ). Answer: According to [1, p. 43], cos( x ) = cos( x ), but sin( x ) = sin( x ). Compare also the graphs of the functions on the same page; Inv ips the graph of a function over around the y-axis....
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- Fall '11