Unformatted text preview: L is equal to the slope of the tangent line (two lines through P of the same slope necessarily coincide). The slope of L is slope of L = 2-(1-cos t ) t-( t-sin t ) = 1 + cos t sin t The slope of the tangent line at P is dy dx = y ( t ) x ( t ) = (1-cos t ) ( t-sin t ) = sin t 1-cos t These two slope are equal: 1 + cos t sin t = sin t 1-cos t because 1-cos 2 t = sin 2 t . This completes the proof....
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This note was uploaded on 10/26/2011 for the course MATH 32A taught by Professor Gangliu during the Spring '08 term at UCLA.
- Spring '08