**Find an equation for the line tangent to the curve at the point defined by the…**

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## Question “Find an equation for the line tangent to the curve at the point defined by the…”

Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of at this point x=16 cost, y = 4 sint,t= The equation represents the line tangent to the curve at t= (Type an exact answer, using radicals as needed.) d²y The value of dx2 (Type an exact answer, using radicals as needed.) att =

## Answer

sos) Given, = usint z=1/4 x=16 cost; de Ciscost] =-16sint dy z = 2 1 [usint}= 4cost – slope m2 dyldt duldt 4 cost -16 sint I h cot(t) – 1 cot (1/6) 2 ot ald yo Now 2=16 cos (1/4) = 16 v2 (214) =( 16 ) m = – – – – = 48 sint = 5 m=-52 4 equation is g- u (x-16 / Vz 4 >> y – 4 / 2x 4 + 4 4 > y = 4+ . 2x ola 4 y + 2x 4+ V2

tangent -ot equation y + 2x – 4 4 b Now du d dy dt dx dt du dan 16 sint & [ (606) =cosce” (t), 4 losint cosec 3 (t) at t=1/4 64 (12) 64 dy da2 v2 32

## Conclusion

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