It is given that , and are the stationary points, we need to find the values of at , and .
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We know that when a curve is given in parametric form, in terms of the parameter we can use the chain rule to find in terms of .
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Now,
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Now,
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Since
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[Using , and ]
\n\n\n\n\n\n\n\n\n\n
Hence, .
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Now, for the stationary points we must have
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radians
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We can see that the point lies in the fourth quadrant. So, from equation , we have
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Hence, the required values of at , and are and respectively.
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\n"},"comment":{"@type":"Comment","text":"
Recall that when a curve is given in parametric form, in terms of the parameter we can use the chain rule to find in terms of i.e., . And, recall that the stationary points are the points on a curve where the gradient is zero.
The parametric equations of a curve are for The curve crosses the -axis at the points and and the stationary points are and as shown in the diagram.
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Find the values of at and giving each answer correct to decimal places.
\n"},"name":"Quiz on Differentiation","typicalAgeRange":"10-17","url":"https://www.embibe.com/questions/%0AThe-parametric-equations-of-a-curve-are-x%3D6sin2t%2C%C2%A0y%3D2sin%C2%A02t%2B3cos%C2%A02t-for-0%E2%A9%BDt%3C%CF%80-The-curve-crosses-the-x--axis-at-the-points-B-and-D-and-the-stationary-points-are-A-and-C%2C-as-shown-in-the-diagram.%0AFind-the-values-of-t-atA--and-C%2C-giving-each-answer-correct-to-3-decimal-places.%0A/EM8257163"}
Sue Pemberton Mathematics Solutions for Exercise - Sue Pemberton, Julianne Hughes and, Julian Gilbey Solutions for Chapter: Differentiation, Exercise 9: END-OF-CHAPTER REVIEW EXERCISE 4
Attempt the free practice questions on Chapter 4: Differentiation, Exercise 9: END-OF-CHAPTER REVIEW EXERCISE 4 with hints and solutions to strengthen your understanding. Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book solutions are prepared by Experienced Embibe Experts.
Questions from Sue Pemberton, Julianne Hughes and, Julian Gilbey Solutions for Chapter: Differentiation, Exercise 9: END-OF-CHAPTER REVIEW EXERCISE 4 with Hints & Solutions