soullesstempt5468 soullesstempt5468

22-06-2018
Mathematics

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Find the exact slope of the tangent line to the parametric curve { x = 7 cos ( t ) y = 5 sin ( t ) {x=7cos(t)y=5sin(t) at the point where t = π 6 t=π6.

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sqdancefan sqdancefan

01-07-2018

The slope of the line will be
m = (dy/dt)/(dx/dt)
= 5·cos(t)/(-7·sin(t))
= (-5/7)·cot(t)

For t=π/6, this is
m = (-5/7)√3

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