To determine Calculate the points in the interior of the first quadrant and calculate the two tangent line equations at the origin. Explanation Given data: x = sin 2 t (1) y = sin 3 t (2) Calculation: Find d x d t . d x d t = d d t [ sin 2 t ] = 2 cos 2 t Find d y d t . d y d t = d d t [ sin 3 t ] = 3 cos 3 t Find d y d x . d y d x = ( d y d t ) ( d x d t ) Substitute 2 cos 2 t for d x d t and 3 cos 3 t for d y d t as follows. d y d x = 3 cos 3 t 2 cos 2 t (3) d y d x = 3 ( cos 2 t cos t − sin 2 t sin t ) 2 ( 2 cos 2 t − 1 ) = 3 [ ( 2 cos 2 t − 1 ) cos t − 2 sin t cos t sin t ] 2 ( 2 cos 2 t − 1 ) = ( 3 cos t ) ( 2 cos 2 t − 1 − 2 sin 2 t ) 2 ( 2 cos 2 t − 1 ) = ( 3 cos t ) ( 4 cos 2 t − 3 ) 2 ( 2 cos 2 t − 1 ) Substitute 0 for d y d x as follows

Thomas' Calculus: Early Transcendentals, Books a la Carte Edition (14th Edition)

14th Edition

ISBN: 9780134439440

Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher: PEARSON

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Chapter 11.2, Problem 46E

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Calculate the points in the interior of the first quadrant and calculate the two tangent line equations at the origin.

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Chapter 11.2, Problem 45E

Chapter 11.2, Problem 47E

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Thomas' Calculus: Early Transcendentals, Books a la Carte Edition (14th Edition)

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