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Question
Find the derivatives of the following:
x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`
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Solution
x = a cost , y = a sin3t
`("d"x)/("d"t) = 3"a"cos^2"t" (- sin"t")`, `("d"y)/("dt") = 3 "a"sin^2"t" (cos "t")`
`(("d"y)/("dt"))/(("d"x)/("dt")) = (3"a" sin^2"t" cos"t")/(- 3"a" cos^2"t" sin"t")`
`("d"y)/("d"x) = - (sin "t")/(cos "t")`
`("d"y)/("d"x)` = – tan t
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