Determine the equation of the tangent line to the given path at the specified va

shadsiei 2021-10-28 Answered
Determine the equation of the tangent line to the given path at the specified value of t.
(sin3t,cos3t,2t52);t=1
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Expert Answer

Tasneem Almond
Answered 2021-10-29 Author has 91 answers
Remember that for a path c(t) the equation of its tangent line at the point c(t0) is given with:
l(t)=c(t0)+c(t0)(tt0)
In our case c(t)=(sin3t,cos3t,2t52) and t0=1
To obtain c'(t) calculate the derivatives component-wise:
c(t)=((sin3t),(cos3t),(2t52))=(3cos3t,3sin3t,5t32)
Which gives:
c(1)=(3cos3,3sin3,5)
Finally, using (1) we have:
l(t)=c(1)+c(1)(t1)
I.e.
l(t)=(sin3,cos3,2)+(3cos33sin3,5)(t1)
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