Explanation Given: c ( t ) = ( t + sin t , t − 2 sin t ) where the tangent is vertical or horizontal . Calculation: It is given that c ( t ) = ( t + sin t , t − 2 sin t ) that means we have x ( t ) = t + sin t , y ( t ) = t − 2 sin t Now, differentiate both the equations x ( t ) = t + sin t , y ( t ) = t − 2 sin t with respect to t and we get: x ( t ) = t + sin t , y ( t ) = t − 2 sin t d x d t = 1 + cos t , d y d t = 1 − 2 cos t Now, we have to find out d y d x So, d y d x = d y d t d x d t = 1 − 2 cos t 1 + cos t Now, the tangent will be horizontal at points where: 1 − 2 cos t = 0 and 1 + cos t ≠ 0 cos t = 1 2 and cos t ≠ − 1 t = π 3 , 5 π 3 and t ≠ π Thus, the tangent is horizontal to the given curve at the points: ( t + sin t

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ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 12, Problem 18CRE

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The points on $(t + \sin t, t - 2 \sin t)$ where the tangent is vertical or horizontal

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Chapter 12, Problem 17CRE

Chapter 12, Problem 19CRE

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Chapter 12 Solutions

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Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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The points on ( t + sin t , t − 2 sin t ) where the tangent is vertical or horizontal

Solution Summary: The author explains how the tangent is horizontal to the given curve at the points: (t + sin t) and ( 3 + 3 2,

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The points on $(t + \sin t, t - 2 \sin t)$ where the tangent is vertical or horizontal

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Chapter 12 Solutions

The points on ( t + sin t , t − 2 sin t ) where the tangent is vertical or horizontal

Solution Summary: The author explains how the tangent is horizontal to the given curve at the points: (t + sin t) and ( 3 + 3 2,

Videos

The points on (t+sint,t−2sint)<math><mrow><mrow><mo>(</mo><mrow><mi>t</mi><mo>+</mo><mi>sin</mi><mi>t</mi><mo>,</mo><mi>t</mi><mo>−</mo><mn>2</mn><mi>sin</mi><mi>t</mi></mrow><mo>)</mo></mrow></mrow></math> where the tangent is vertical or horizontal

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Chapter 12 Solutions

The points on $(t + \sin t, t - 2 \sin t)$ where the tangent is vertical or horizontal